intermediate algreba

Question

Suppose you want to build a rectangular picture frame where the width is 2 centimeters less than the length and the diagonal is 2 centimeters longer than the length. What are the dimensions of the picture frame?

Answer 1

W = L-2

D = L+2

D^2 = W^2 + L^2

(L+2)^2 = (L-2)^2 + L^2

L^2 +4L + 4 = L^2 -4L + 4 + L^2

L^2 -8L = 0

L(L-8) = 0

L= 8 cm long

W = 6 cm wide

D=10 cm = the diagonal

10^2 = 8^2 + 6^2

100 = 64 +36

Ignore the L=0 solution, as it makes W negative