Suppose you want to draw a rectangle where the width is 4 centimeters less than the length and the diagonal is 4 centimeters longer than the length. What are the dimensions of the rectangle?

Answer 1

W=L-4

D=4+L

D^2 = L^2 + W^2 = L^2 + (L-4)^2 = L^2 + L^2 -8L + 16

= 2L^2 -8L +16

(L+4)^2 = L^2 + 8L + 16

= 2L^2 -8L +16

subtract to get

L^2 -16L = 0

factor

L(L-16) = 0

L-16=0

L=16 cm long

W= 12 cm wide

D = 20 cm diagonal

20^2 = 16^2 + 12^2

400 = 256 + 144

ignore the L=0 cm solution, unless you're in the twilight zone with W= -4 cm and D= 4 cm

4^2 = 0^2 + (-4)^2