Question

What is the area of a rectangle whose length is twice its width and whose perimeter is equal to that of a square whose area is 1?

Answer 1

Area of sq= 1unit²= (side)²

Side= √1= 1unit

Perimeter of sq.= 4× side= 4×1= 4unit

Perimeter of rectangle= perimeter of square= 4unit

Let width of rectangle be x

Length of rectangle= 2x

Perimeter= 2(l+b)

4= 2(x+2x)

2= 3x

x= 2/3unit= width

Length= 2x= 4/3unit

Area= l×b= (2/3)×(4/3)=8/9unit²