Problema Solution
A square and rectangle have the same area. The length of a rectangle is five inches more than twice the length of the side of the square. The width of the rectangle is six inches less than the side of the square. Find the length of the side of the square.
Answer provided by our tutors
let
a = the length of the side of the square, a>0
w = the width of the rectangle
l = the length of the rectangle
A square and rectangle have the same area
a^2 = l*w
The length of a rectangle is five inches more than twice the length of the side of the square
l = 5 + 2a
The width of the rectangle is six inches less than the side of the square
w = a - 6
plug l = 5 + 2a and w = a - 6 into a^2 = l*w we get
a^2 = (5 + 2a)(a - 6)
by solving we find
a = 10 in
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the length of the side of the square is 10 inches.