Question

the differece between the sides at right angles in a right angled triangle is 7cm . the area of the triangle is 60 cm square . find its perimeter.

Answer 1

Let one side be x
Other is x-7

Area of traingle = 1/2 * b * h
= 0.5 * x * (x-7) = 60

Multiply both sides by 2
x*(x-7)=120
x^2 - 7x - 120 = 0

(x-15)(x+8)= 0

So x = 15 since x cant be negative
x-7= 8

Using Pythagoras theorem,
64 + 225 = h*h
h=17
Perimeter = 17+15+8 = 40cm

Answer 2

let a , b be the sides....
so a-b= 7cm
I.e. a = b + 7
also area = 60 cm^2
so 1/2 × a × b = 60
a × b = 120
as, a = b + 7,
(b+7) (b) = 120
b^2 + 7b - 120 = 0

so, b = 8
and a = 15