The length of a rectangle is 2 m less than the diagonal and the width is 8 m less than the diagonal. If the area is 82 m2, how long is the diagonal?
L w = 82
d^2= (L^2+w^2)
but L = d-2 and w = d-8
L^2 = d^2 -4 d + 4
w^2 = d^2 -16 d + 64
so
L^2+w^2 = 2d^2-20d+68 = d^2
so
d^2 - 20d + 68 = 0
d = [ 20 +/-sqrt(400-272)]2
d = 10 +/- 5.66
d must be bigger than 8 so
d = 15.66
check my arithmetic