###### Advertisements

###### Advertisements

**Choose the correct alternative:**

If length of sides of a triangle are a, b, c and a^{2} + b^{2} = c^{2}, then which type of triangle it is?

#### Options

Obtuse angled triangle

Acute angled triangle

Equilateral triangle

Right angled triangle

###### Advertisements

#### Solution

**Right angled triangle**

#### RELATED QUESTIONS

In triangle ABC, ∠C=90°. Let BC= a, CA= b, AB= c and let 'p' be the length of the perpendicular from 'C' on AB, prove that:

1. cp = ab

2. `1/p^2=1/a^2+1/b^2`

Prove that the diagonals of a rectangle ABCD, with vertices A(2, -1), B(5, -1), C(5, 6) and D(2, 6), are equal and bisect each other.

From a point O in the interior of a ∆ABC, perpendicular OD, OE and OF are drawn to the sides BC, CA and AB respectively. Prove

that :

`(i) AF^2 + BD^2 + CE^2 = OA^2 + OB^2 + OC^2 – OD^2 – OE^2 – OF^2`

`(ii) AF^2 + BD^2 + CE^2 = AE^2 + CD^2 + BF^2`

PQR is a triangle right angled at P and M is a point on QR such that PM ⊥ QR. Show that PM^{2} = QM . MR

Prove that the sum of the squares of the sides of a rhombus is equal to the sum of the squares of its diagonals

In the following figure, O is a point in the interior of a triangle ABC, OD ⊥ BC, OE ⊥ AC and OF ⊥ AB. Show that

(i) OA^{2} + OB^{2} + OC^{2} − OD^{2} − OE^{2} − OF^{2} = AF^{2} + BD^{2} + CE^{2}

(ii) AF^{2} + BD^{2} + CE^{2 }= AE^{2} + CD^{2} + BF^{2}

In an equilateral triangle ABC, D is a point on side BC such that BD = `1/3BC` . Prove that 9 AD^{2} = 7 AB^{2}

In an equilateral triangle, prove that three times the square of one side is equal to four times the square of one of its altitudes.

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 cm, 2 cm, 5 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

The perimeter of a triangle with vertices (0, 4), (0, 0) and (3, 0) is

(A)\[7 + \sqrt{5}\]

(B) 5

(C) 10

(D) 12

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

(3, 5, 4)

**Identify, with reason, if the following is a Pythagorean triplet.**(5, 12, 13)

**Identify, with reason, if the following is a Pythagorean triplet.**(10, 24, 27)

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 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.

Find the length of the hypotenuse of a right angled triangle if remaining sides are 9 cm and 12 cm.

In ∆ABC, seg AD ⊥ seg BC, DB = 3CD.

Prove that: 2AB^{2 }= 2AC^{2 }+ 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.

In a trapezium ABCD, seg AB || seg DC seg BD ⊥ seg AD, seg AC ⊥ seg BC, If AD = 15, BC = 15 and AB = 25. Find A(▢ABCD)

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.

**In ΔABC, Find the sides of the triangle, if:**

- AB = ( x - 3 ) cm, BC = ( x + 4 ) cm and AC = ( x + 6 ) cm
- AB = x cm, BC = ( 4x + 4 ) cm and AC = ( 4x + 5) cm

**Two poles of heights 6 m and 11 m stand vertically on a plane ground. If the distance between their feet is 12 m;**

find the distance between their tips.

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

**In the figure, given below, AD ⊥ BC. **Prove that: c

^{2}= a

^{2}+ b

^{2}- 2ax.

**In triangle ABC, angle A = 90 ^{o}, CA = AB and D is the point on AB produced.**

Prove that DC

^{2}- BD

^{2}= 2AB.AD.

In equilateral Δ ABC, AD ⊥ BC and BC = x cm. Find, in terms of x, the length of AD.

**ABC is a triangle, right-angled at B. M is a point on BC.**

Prove that: AM^{2} + BC^{2} = AC^{2} + BM^{2}.

**O is any point inside a rectangle ABCD.**

Prove that: OB^{2} + OD^{2} = OC^{2} + OA^{2}.

**In a quadrilateral ABCD, ∠B = 90° and ∠D = 90°.**

Prove that: 2AC^{2} - AB^{2} = BC^{2} + CD^{2} + DA^{2}

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

Find the side of the square whose diagonal is `16sqrt(2)` cm.

Prove that in a right angle triangle, the square of the hypotenuse is equal to the sum of squares of the other two sides.

Triangle ABC is right-angled at vertex A. Calculate the length of BC, if AB = 18 cm and AC = 24 cm.

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

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

16 cm, 20 cm, and 12 cm

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: PR, if PQ = 8 cm and QR = 6 cm

In the given figure, angle ACB = 90° = angle ACD. If AB = 10 m, BC = 6 cm and AD = 17 cm, find :

(i) AC

(ii) CD

In the given figure, angle ADB = 90°, AC = AB = 26 cm and BD = DC. If the length of AD = 24 cm; find the length of BC.

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?

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

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

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.

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

3, 4, 5

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

2, 6, 7

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

9, 40, 41

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

4, 7, 8

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

11, 12, 15

From the given figure, find the length of hypotenuse AC and the perimeter of ∆ABC.

Find the length of the hypotenuse of a triangle whose other two sides are 24cm and 7cm.

In a triangle ABC, AC > AB, D is the midpoint BC, and AE ⊥ BC. Prove that: AC^{2} = AD^{2 }+ BC x DE + `(1)/(4)"BC"^2`

In a triangle ABC, AC > AB, D is the midpoint BC, and AE ⊥ BC. Prove that: AB^{2} + AC^{2} = 2AD^{2 }+ `(1)/(2)"BC"^2`

A point OI in the interior of a rectangle ABCD is joined with each of the vertices A, B, C and D. Prove that OB^{2} + OD^{2 }= OC^{2} + OA^{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 : 9(AQ^{2} + BP^{2}) = 13AB^{2}

In the given figure. PQ = PS, P =R = 90°. RS = 20 cm and QR = 21 cm. Find the length of PQ correct to two decimal places.

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

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 in a ΔPQR, PR^{2} = PQ^{2} + QR^{2}, then the right angle of ∆PQR is at the vertex ________

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

In triangle ABC, line I, is a perpendicular bisector of BC.

If BC = 12 cm, SM = 8 cm, find CS

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

In the figure, find AR

In an equilateral triangle PQR, prove that PS^{2} = 3(QS)^{2}.

In a right-angled triangle ABC, if angle B = 90°, then which of the following is true?

Two squares are congruent, if they have same ______.

A right-angled triangle may have all sides equal.

If the areas of two circles are the same, they are congruent.

Two squares having same perimeter are congruent.

Jiya walks 6 km due east and then 8 km due north. How far is she from her starting place?

Points A and B are on the opposite edges of a pond as shown in figure. To find the distance between the two points, the surveyor makes a right-angled triangle as shown. Find the distance AB.

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.