Flower bed question

Question

1. A rectangular flower bed is to be created so that the length is 3 m more than the width. If the length of the diagonal of the flower bed is 15 m, determine the length and the width. (5 marks)

Please answer in full detail

Answer 1

L=3+W

Pythagorean Theorm for D, the Diagonal

D^2 = L^2 +W^2

= (3+W)^2 +W^2

= 9+6W +2W^2

= 15^2= 225

2W^2 +6W -225+9=0

2W^2 +6W - 216 = 0

divide by 2

W^2 +3W -108 = 0

factor

(W+12)(W-9) =0

set each factor =0

W-9=0

W= 9 meters wide

L=W+3 = 12 meters long