Question

The ratio of the shorter side pf a right angled triangle is 5:12.If the perimeter of the triangle is 420cm,find the length of the longest side. please give step by step explanation.​

Answer 1

Answer:

Hypotenuse is the longest side of right angled triangle.

Let the two other sides, which are in fact the shorter sides, be ‘5x’ cm & ‘12x’ cm

Let the hypotenuse be ‘h’cm

Applying Pythagoras theorem,

(5x)^2 + (12x)^2 = h^2

=> 125x^2 + 144x^2 = h^2

=> h^2 = 169x^2

=> h = 13x (Taking square root of both sides)

Since, perimeter = 420,

5x + 12x + 13x= 420

=> 30x=420

=>x = 14

Therefore, longest side = hypotenuse = h =13x=13 into 14=182 cm

Ans = 182 cm