Quadratic formula

Question

Suppose you want to draw a rectangle where the width is 22 centimeters less than the length and the diagonal is 22 centimeters longer than the length. What are the dimensions of the rectangle?

Answer 1

w=L-22

L=w+22

d=L+22=w+22+22= w+44

d^2= (w+44)^2 = w^2+88w+44^2

d^2=L^2 +w^2

d^2= (w+22)^2 +w^2

d^2= 2w^2+44w+22^2 = w^2+88w+44^2

w^2 -44w = 44^2 -22^2

w^2 -44w = 2420

w^2 -44w + 22^2 = 44^2-22^2 +22^2

(w-22)^2 = 44^2

w -22 = 44

w = 44+22 = 66 cm Wide

L =88 cm Long

D= 110 cm Diagonal

66^2 + 88^2 = 12100 = 110