The length of a rectangle is 3 m less than the diagonal and the width is 8 m less than the diagonal. If the area is 84 m2, how long is the diagonal? Round your answer to the nearest tenth.

Answer 1

L^2 + w^2 = d^2

(d-3)^2 + (d-8)^2 = d^2

d^2 - 6 d + 9 + d^2 -16 d + 64 = d^2

d^2 - 22 d + 73 = 0

d = [ 22 +/- sqrt(484 - 292) ] / 2

d = [ 22 +/- 13.9 ] / 2

d = 17.9 or 8.1

8.1 is impossible if the area is 84 so d = 17.9
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check
then w = about 10 and L = about 15
so area = 150 m^2

beats me