###### Advertisements

###### Advertisements

**The sides of a certain triangle is given below. Find, which of them is right-triangle**

16 cm, 20 cm, and 12 cm

###### Advertisements

#### Solution

16 cm, 20 cm and 12 cm

The given triangle will be a right-angled triangle if square of its largest side is equal to the sum of the squares on the other two sides.

i.e., If (20)^{2} = (16)^{2} = (12)^{2}(20)^{2} = (16)^{2} + (12)^{2}400 = 256 + 144

400 = 400

So, the given triangle is right-angled.

#### APPEARS IN

#### RELATED QUESTIONS

If the sides of a triangle are 6 cm, 8 cm and 10 cm, respectively, then determine whether the triangle is a right angle triangle or not.

A ladder leaning against a wall makes an angle of 60° with the horizontal. If the foot of the ladder is 2.5 m away from the wall, find the length of the ladder

A man goes 10 m due east and then 24 m due north. Find the distance from the starting point

In a ∆ABC, AD ⊥ BC and AD^{2} = BC × CD. Prove ∆ABC is a right triangle

Sides of triangles are given below. Determine it is a right triangles? In case of a right triangle, write the length of its hypotenuse. 3 cm, 8 cm, 6 cm

In Figure ABD is a triangle right angled at A and AC ⊥ BD. Show that AC^{2} = BC × DC

A guy wire attached to a vertical pole of height 18 m is 24 m long and has a stake attached to the other end. How far from the base of the pole should the stake be driven so that the wire will be taut?

Prove that the sum of the squares of the diagonals of parallelogram is equal to the sum of the squares of its sides.

Which of the following can be the sides of a right triangle?

2.5 cm, 6.5 cm, 6 cm

In the case of right-angled triangles, identify the right angles.

The diagonals of a rhombus measure 16 cm and 30 cm. Find its perimeter.

Prove that, in a right-angled triangle, the square of the hypotenuse is equal to the sum of the square of remaining two sides

**Identify, with reason, if the following is a Pythagorean triplet.**

(11, 60, 61)

Find the side and perimeter of a square whose diagonal is 10 cm ?

Walls of two buildings on either side of a street are parellel to each other. A ladder 5.8 m long is placed on the street such that its top just reaches the window of a building at the height of 4 m. On turning the ladder over to the other side of the street , its top touches the window of the other building at a height 4.2 m. Find the width of the street.

In ∆ABC, AB = 10, AC = 7, BC = 9, then find the length of the median drawn from point C to side AB.

In the given figure, point T is in the interior of rectangle PQRS, Prove that, TS^{2 }+ TQ^{2 }= TP^{2 }+ TR^{2 }(As shown in the figure, draw seg AB || side SR and A-T-B)

Some question and their alternative answer are given. Select the correct alternative.

If a, b, and c are sides of a triangle and a^{2 }+ b^{2 }= c^{2}, name the type of triangle.

In ∆ABC, ∠BAC = 90°, seg BL and seg CM are medians of ∆ABC. Then prove that:

4(BL^{2 }+ CM^{2}) = 5 BC^{2}

^{}

In an isosceles triangle, length of the congruent sides is 13 cm and its base is 10 cm. Find the distance between the vertex opposite the base and the centroid.

Digonals of parallelogram WXYZ intersect at point O. If OY =5, find WY.

In right angle ΔABC, if ∠B = 90°, AB = 6, BC = 8, then find AC.

**A man goes 40 m due north and then 50 m due west. Find his distance from the starting point.**

**The given figure shows a quadrilateral ABCD in which AD = 13 cm, DC = 12 cm, BC = 3 cm and ∠ABD = ∠BCD = 90 ^{o}. Calculate the length of AB.**

**In triangle ABC, AB = AC = x, BC = 10 cm and the area of the triangle is 60 cm ^{2}.**

Find x.

**In triangle ABC, given below, AB = 8 cm, BC = 6 cm and AC = 3 cm. Calculate the length of OC.**

**In an isosceles triangle ABC; AB = AC and D is the point on BC produced.**

Prove that: AD^{2} = AC^{2} + BD.CD.

**Diagonals of rhombus ABCD intersect each other at point O. **

Prove that: OA^{2} + OC^{2} = 2AD^{2} - `"BD"^2/2`

Choose the correct alternative:

In right-angled triangle PQR, if hypotenuse PR = 12 and PQ = 6, then what is the measure of ∠P?

Find the length of diagonal of the square whose side is 8 cm.

In Fig. 3, ∠ACB = 90° and CD ⊥ AB, prove that CD^{2} = BD x AD.

Triangle XYZ is right-angled at vertex Z. Calculate the length of YZ, if XY = 13 cm and XZ = 12 cm.

Triangle PQR is right-angled at vertex R. Calculate the length of PR, if: PQ = 34 cm and QR = 33.6 cm.

**The sides of a certain triangle is given below. Find, which of them is right-triangle**

6 m, 9 m, and 13 m

In the given figure, angle BAC = 90°, AC = 400 m, and AB = 300 m. Find the length of BC.

In triangle PQR, angle Q = 90°, find: PQ, if PR = 34 cm and QR = 30 cm

Show that the triangle ABC is a right-angled triangle; if: AB = 9 cm, BC = 40 cm and AC = 41 cm

In the given figure, AD = 13 cm, BC = 12 cm, AB = 3 cm and angle ACD = angle ABC = 90°. Find the length of DC.

A ladder, 6.5 m long, rests against a vertical wall. If the foot of the ladder is 2.5 m from the foot of the wall, find up to how much height does the ladder reach?

A boy first goes 5 m due north and then 12 m due east. Find the distance between the initial and the final position of the boy.

Use the information given in the figure to find the length AD.

In the figure below, find the value of 'x'.

In the right-angled ∆PQR, ∠ P = 90°. If l(PQ) = 24 cm and l(PR) = 10 cm, find the length of seg QR.

In the right-angled ∆LMN, ∠M = 90°. If l(LM) = 12 cm and l(LN) = 20 cm, find the length of seg MN.

The top of a ladder of length 15 m reaches a window 9 m above the ground. What is the distance between the base of the wall and that of the ladder?

Find the Pythagorean triplet from among the following set of numbers.

2, 4, 5

Find the Pythagorean triplet from among the following set of numbers.

4, 5, 6

Find the Pythagorean triplet from among the following set of numbers.

2, 6, 7

The sides of the triangle are given below. Find out which one is the right-angled triangle?

11, 12, 15

The sides of the triangle are given below. Find out which one is the right-angled triangle?

1.5, 1.6, 1.7

The sides of the triangle are given below. Find out which one is the right-angled triangle?

40, 20, 30

A ladder 15m long reaches a window which is 9m above the ground on one side of a street. Keeping its foot at the same point, the ladder is turned to other side of the street to reach a window 12m high. Find the width of the street.

The foot of a ladder is 6m away from a wall and its top reaches a window 8m above the ground. If the ladder is shifted in such a way that its foot is 8m away from the wall to what height does its tip reach?

Each side of rhombus is 10cm. If one of its diagonals is 16cm, find the length of the other diagonals.

In ΔABC, AD is perpendicular to BC. Prove that: AB^{2} + CD^{2} = AC^{2} + BD^{2}

In an equilateral triangle ABC, the side BC is trisected at D. Prove that 9 AD^{2 }= 7 AB^{2}.

From a point O in the interior of aΔABC, perpendicular OD, OE and OF are drawn to the sides BC, CA and AB respectively. Prove that: AF^{2} + BD^{2} + CE^{2 }= OA^{2} + OB^{2} + OC^{2} - OD^{2} - OE^{2} - OF^{2}

In a triangle ABC, AC > AB, D is the midpoint BC, and AE ⊥ BC. Prove that: AB^{2} + AC^{2} = 2(AD^{2} + CD^{2})

In a triangle ABC right angled at C, P and Q are points of sides CA and CB respectively, which divide these sides the ratio 2 : 1.

Prove that: 9AQ^{2 }= 9AC^{2} + 4BC^{2}

In the given figure, PQ = `"RS"/(3)` = 8cm, 3ST = 4QT = 48cm.

SHow that ∠RTP = 90°.

In a right-angled triangle ABC,ABC = 90°, AC = 10 cm, BC = 6 cm and BC produced to D such CD = 9 cm. Find the length of AD.

PQR is an isosceles triangle with PQ = PR = 10 cm and QR = 12 cm. Find the length of the perpendicular from P to QR.

Determine whether the triangle whose lengths of sides are 3 cm, 4 cm, 5 cm is a right-angled triangle.

A man goes 18 m due east and then 24 m due north. Find the distance of his current position from the starting point?

There are two paths that one can choose to go from Sarah’s house to James's house. One way is to take C street, and the other way requires to take B street and then A street. How much shorter is the direct path along C street?

To get from point A to point B you must avoid walking through a pond. You must walk 34 m south and 41 m east. To the nearest meter, how many meters would be saved if it were possible to make a way through the pond?

The perpendicular PS on the base QR of a ∆PQR intersects QR at S, such that QS = 3 SR. Prove that 2PQ^{2} = 2PR^{2} + QR^{2}

Two trains leave a railway station at the same time. The first train travels due west and the second train due north. The first train travels at a speed of `(20 "km")/"hr"` and the second train travels at `(30 "km")/"hr"`. After 2 hours, what is the distance between them?

If ‘l‘ and ‘m’ are the legs and ‘n’ is the hypotenuse of a right angled triangle then, l^{2} = ________

In a right angled triangle, the hypotenuse is the greatest side

Find the unknown side in the following triangles

Find the unknown side in the following triangles

Find the unknown side in the following triangles

An isosceles triangle has equal sides each 13 cm and a base 24 cm in length. Find its height

Find the distance between the helicopter and the ship

The hypotenuse of a right angled triangle of sides 12 cm and 16 cm is __________

Find the length of the support cable required to support the tower with the floor

Rithika buys an LED TV which has a 25 inches screen. If its height is 7 inches, how wide is the screen? Her TV cabinet is 20 inches wide. Will the TV fit into the cabinet? Give reason

From the given figure, in ∆ABQ, if AQ = 8 cm, then AB =?

In a right angled triangle, if length of hypotenuse is 25 cm and height is 7 cm, then what is the length of its base?

Foot of a 10 m long ladder leaning against a vertical wall is 6 m away from the base of the wall. Find the height of the point on the wall where the top of the ladder reaches.

In a quadrilateral ABCD, ∠A + ∠D = 90°. Prove that AC^{2} + BD^{2} = AD^{2} + BC^{2}

[**Hint:** Produce AB and DC to meet at E.]

In an isosceles triangle PQR, the length of equal sides PQ and PR is 13 cm and base QR is 10 cm. Find the length of perpendicular bisector drawn from vertex P to side QR.

Lengths of sides of a triangle are 3 cm, 4 cm and 5 cm. The triangle is ______.

Two angles are said to be ______, if they have equal measures.

Two squares having same perimeter are congruent.

Two circles having same circumference are congruent.

If two legs of a right triangle are equal to two legs of another right triangle, then the right triangles are congruent.

Two poles of 10 m and 15 m stand upright on a plane ground. If the distance between the tops is 13 m, find the distance between their feet.

The foot of a ladder is 6 m away from its wall and its top reaches a window 8 m above the ground. Find the length of the ladder.