Advertisements
Advertisements
Question
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.
Advertisements
Solution
The sides of the triangle are 6 cm, 8 cm and 10 cm.
The longest side is 10 cm.
(10)2 = 100 ….(i)
Now, the sum of the squares of the other two sides will be,
(6)2 + (8)2 = 36 + 64 = 100 ….(ii)
(10)2 = (6)2 + (8)2 ….. from (i) and (ii)
By the converse of Pythagoras theorem:
The given sides form a right angled triangle.
APPEARS IN
RELATED QUESTIONS
In a ∆ABC, AD ⊥ BC and AD2 = BC × CD. Prove ∆ABC is a right triangle
In the given figure, ABC is a triangle in which ∠ABC> 90° and AD ⊥ CB produced. Prove that AC2 = AB2 + BC2 + 2BC.BD.
Identify, with reason, if the following is a Pythagorean triplet.
(24, 70, 74)
Find the side and perimeter of a square whose diagonal is 10 cm.
In the figure, given below, AD ⊥ BC.
Prove that: c2 = a2 + b2 - 2ax.
O is any point inside a rectangle ABCD.
Prove that: OB2 + OD2 = OC2 + OA2.
Find the side of the square whose diagonal is `16sqrt(2)` cm.
In Fig. 3, ∠ACB = 90° and CD ⊥ AB, prove that CD2 = BD x AD.
Prove that `(sin θ + cosec θ)^2 + (cos θ + sec θ)^2 = 7 + tan^2 θ + cot^2 θ`.
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.
Find the Pythagorean triplet from among the following set of numbers.
2, 6, 7
Find the length of the perpendicular of a triangle whose base is 5cm and the hypotenuse is 13cm. Also, find its area.
In a triangle ABC, AC > AB, D is the midpoint BC, and AE ⊥ BC. Prove that: AB2 = AD2 - BC x CE + `(1)/(4)"BC"^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: 9AQ2 = 9AC2 + 4BC2
The perpendicular PS on the base QR of a ∆PQR intersects QR at S, such that QS = 3 SR. Prove that 2PQ2 = 2PR2 + QR2
Find the unknown side in the following triangles
In the given figure, AD is a median of a triangle ABC and AM ⊥ BC. Prove that:
(i) `"AC"^2 = "AD"^2 + "BC"."DM" + (("BC")/2)^2`
(ii) `"AB"^2 = "AD"^2 - "BC"."DM" + (("BC")/2)^2`
(iii) `"AC"^2 + "AB"^2 = 2"AD"^2 + 1/2"BC"^2`
The hypotenuse (in cm) of a right angled triangle is 6 cm more than twice the length of the shortest side. If the length of third side is 6 cm less than thrice the length of shortest side, then find the dimensions of the triangle.
Height of a pole is 8 m. Find the length of rope tied with its top from a point on the ground at a distance of 6 m from its bottom.
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.
