Question

two sides of a rectangle are X + 2 and 4 x if the length of the diagonal is 13 cm then what is the area of the rectangle

Answer 1

Rectangle  sides and diagonal form a right angled triangle.    Using pythagorean theorem       P^2 + B^2 = H^2

(x + 2)^2 + (4x)^2  = 13^2

x^2 + 4x + 4 + 16x^2 = 169

17x^2 + 4x  - 165 = 0

17x^2 - 51x + 55x - 165 = 0

(x - 3)(17x + 55) = 0

x =3, x = -55/17

so x = 3,          

sides become  3+2 = 5  ,     and   4x = 4*3 = 12

Area  = L X B = 5 * 12 = 60 cm^2