What is the area of a rectangle whose length is twice it's width and whose perimeter is equal to the perimeter of a square whose area is 1m (square)?

Question

Please explain.

Answer 1

area of rectangle = length times width

A = (L)(W)

 

length = twice width

L = 2W

so

A = 2W²

 

perimeter of rectangle = twice the length plus twice the width

P = 2L + 2W

P = 6W

 

perimeter = perimeter of of a square whose area is 1

 

Say one side of the square is S, then S² = 1. So S = 1 and the perimeter is 4.

 

4 = 6W.

W = 4/6

A = 2(4/6)²

A = 2(16/36)

A = 8/9

Answer 2

The perimeter of a square whose area is 1 m² is 4 m.

 

Set the width of the rectangle = x, then the length of the rectangle = 2x.

 

So we have (2x+x)*2 = 4,  thus x = 2/3 m

 

Area of the rectangle = length*width = 2x*x = 2*(2/3)*(2/3) = 8/9 m²