Problema Solution
A square and a rectangle have the same perimeters. the length of a side of the square is 4x-1. The length of the rectangle is 2x+1 and the width is x+2. Write and solve and equation to find x.
Answer provided by our tutors
the perimeter of a square P = 4a, where a is the length of the side
in our case a = 4x - 1 thus the perimeter of the square is:
P1 = 4*(4x - 1)
the perimeter of a rectangle P = 2(w + l), where w is the width of the rectangle and l is the length of the rectangle
in our case l = 2x+1 and w = x+2 thus the perimeter of the rectangle is:
P2 = 2*(2x + 1 + x + 2)
A square and a rectangle have the same perimeters:
P1 = P2
4*(4x - 1) = 2*(2x + 1 + x + 2)
by solving we find:
x = 1
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