Question

The length of each side of a square is 1 centimeter more than the width of the rectangle. The length of the rectangle is 1 centimeter less than twice it’s width. The perimeters of the two figures are equal. Determine the measures of the side lengths of the rectangle.
Please show all work I have a test tomorrow

Answer 1

Let the side of square be s and the length and breadth or width of the rectangle be l and b respectively. (Also, keep in mind that when I am using the * symbol, it stands for multiplication)

s = b + 1

l = 2b - 1

Perimeter of rectangle = 2(l+b) = 2(2b-1+b) = 2(3b-1) = 6b - 2

Perimeter of square = 4(b+1) = 4b + 4

6b - 2 = 4b + 4

6b - 4b = 4 + 2

2b = 6

b = 6/2 = 3 cm

l = (3*2) - 1 = 6 - 1 = 5 cm

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