Question

Please help me to solve this question

Answer 1

Let other sides are x and y.

Since x^2 + y^2 = hypotenuse ^2
x^2 + y^2 = 13^2
x^2 + y^2 = 169 .. 1.

Since 1/2 * x*y = 30
xy = 60 .. 2.

Go in eq. 1.
x^2 + y^2 = 169 .. 1.

(x+y) ^2 - 2xy = 169

= (x+y) ^2 - 2*60 = 169

= (x+y) ^2 = 169+120

= (x+y) ^2 = 289

= (x+y) = 17cm .. 3.

Again in eq. 1.
x^2 + y^2 = 169 .. 1.

= (x-y) ^2 + 2xy = 169

= (x-y) ^2 + 2*60 = 169

= (x-y) ^2 = 169-120

= (x-y) ^2 = 49

= (x-y) = 7cm .. 4.

Add eq. 3and 4.

= x+ y + x - y = 17+7

= 2x = 24

= x = 24/2 = 12cm

Put value of x in eq 3 or 4,

= 12- y= 7

= y = 5cm.

Hence other two sides are 5cm and 12cm.

Hope it's helpful to u.