Question

the diagonal of a rectangle is 60m more than its shorter side and larger side is 30m more than the shorter side.find the sides of a rectangle

Answer 1

let the shorter side is x ,then larger side is x + 30
from pythagoras theorem             (both side are perpendicular)
60^2 = x^2 + (x + 30)^2
3600 = 2x^2 + 60x + 900
x^2 + 30x - 2700 = 0
x = -15 + 5√63,or -15 - 5√63
length of the side can not be negative ,hence
x = -15 + 5√63                     (shorter side)
x + 30 = 15 + 5√63                        (larger side)
hence shorter side is -15 + 5√63 and larger side is 15 + 5√63