Question

if the ratio of the shortest and the longest sides of a right triangle 3:5 and its perimeter is 36 cm, find the area of the triangle.

Answer 1

we know longest side in right angeled triangle is hypotenuse

let the ratio be x

so hypotenuse = 5x

and other short side = 3x

another side considered as y

so by using Pythagoras theorum

hypotenuse ^2 = one side ^2 + another side ^2

(5x)^2 = (3x)^2 + y^2

25x^2 = 9x^2 + y^2

y^2 = 25x^2 - 9x^2

y^2 = 16x^2

y = 4x

so all sides are in ratio

3x : 4x : 5x

perimeter = 36

3x + 4x + 5x = 36

12 x = 36

x = 3

so sides are

3x = 3 × 3 = 9

4x = 4 × 3 = 12

5x = 5 × 3 = 15

area of right angeled triangle = 1/2 × 9 × 12

= 54 sq cm