Question

The diagonal of a rectangle is 60m more than it’s shorter side and the larger side is 30 m more than the shorter side. Find the sides of the rectangle.

Answer 1

let the length of the smaller side = x m

therefore length of the diagonal = (x + 60) m

also length of the larger side = (x + 30) m

A.T.Q

so diagonal divides the rectangle in two rt triangles

therfore by pythagoras,

(diagonal)^2 = (small side)^2 + (large side)^2

(x + 60)^2 = (x + 30)^2 + x^2

x^2 + 3600 + 120x = x^2 + 900 + 60x + x^2

x^2 - 60x -2700 = 0

(x-90)(x + 30) = 0

so x= -30 rejected (as length cannot be -ve)

so x = 90



therefore length of the smaller side = x = 90m

length of the larger side = (x + 30) = 120m