Quadratic equations

Question

The hypotenuse of a right angled triangle is 35 cm. The difference between its other two sides is 7 cm. Find the length of the sides.

Answer 1

one side = x

other side = x + 7

x^2 + (x+7)^2 = 35^2

x^2 + x^2 + 14x + 49 = 1225

2x^2 + 14x -1176 = 0

x^2 +7x - 588 = 0

(x+28)(x-21) = 0

x = 21

Two sides are 21 and 28