Area of the square

Geometry Level 1

A square and a rectangle have the same perimeters. If the shorter side of the rectangle measures 3 feet and the longer side measures 8 feet, what is the area of the square?

see my set : Marvin's Geometry Set


The answer is 30.25.

A Former Brilliant Member by A Former Brilliant Member

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2 solutions

perimeter of the rectangle = 2W + 2L = 2 ∗ 3 + 2 ∗ 8 2*3 + 2*8 = 6 + 16 = 22 feet

perimeter of the square = 4s

22 = 4s

s = 5.5 feet

area of the square = s² = 5.5² = 30.25 feet²

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perimeter of the rectangle = perimeter of the square = 2 ( 8 ) + 2 ( 3 ) = 22 \text{perimeter of the rectangle} = \text{perimeter of the square} = 2(8) + 2(3) = 22

So one side of the square measures 22 4 \dfrac{22}{4} , and the area of the square is ( 22 4 ) 2 = 30.25 \left(\dfrac{22}{4}\right)^2 = \boxed{30.25}

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