Problema Solution
The length of a rectangular floor is 3 meters less than three times its width. If a diagonal of the rectangle is 13 meters, find the length and width of the floor.
Answer provided by our tutors
let
l = the length of the rectangular floor, l>0
w = the width of the rectangular floor, W>0
the length of a rectangular floor is 3 meters less than three times its width
l = 3w - 3
the diagonal of the rectangle is 13 meters and using Pythagorean Theorem we have
w^2 + l^2 = 13^2
by plugin l = 3w - 3 into the above equation we get
w^2 + (3w - 3)^2 = 13^2
by solving the quadratic equation
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we find and consider only the positive roots that is
w = 5 m
l = 3w - 3 = 3*5 - 3 = 15 - 3 = 12
l = 12 m
the length and the width of the floor are 12 meters and 5 meters.