Problema Solution
A square and a rectangle have the same area. The length of the rectangle is 8 less than twice the side of the square. The width of the rectangle is 3 less than the side of the square.
Find the dimensions of the rectangle
Answer provided by our tutors
let
the side of the square: a
the length of the rectangle: 2a - 8
the width of the rectangle: a - 3
the square and the rectangle have same areas
a^2 = (2a - 8)(a - 3)
by solving we find the roots
a1 = 2
a2 = 12
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a1 = 2 is not the solution since we need a - 3 = 2 - 3 = -1<0 to be positive
the length of the rectangle is 2*12 - 8 = 16
the width of the rectangle is 12 - 3 = 9