Problema Solution
The oriental rug shown is 3 feet longer than it is wide. If the diagonal of the rug is 12 feet find its dimensions to the nearest tenth of a foot.
Answer provided by our tutors
we will assume that the rug is rectangular in shape
l = the length of the rectangular rug, l>0
w = the width of the rectangular rug, w>0
d = 12 ft the diagonal of the rug
the oriental rug shown is 3 feet longer than it is wide
l = w + 3
using the Pythagorean Theorem we have
l^2 + w^2 = d^2
plug l = w + 3 into the last equation
(w + 3)^2 + w^2 = 12^2
by solving the quadratic equation we find and consider the positive roots
w = 6.9 ft
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l = w + 3
l = 6.9 + 3
l = 9.9 ft
the dimensions of the rug are 6.9 ft and 9.9 ft.