Question

A unit square and a rectangle have the same perimeter. What is the length of the rectangle if its area is 75% of the square's area?

Answer 1

The rectangle is 9 by 3

The square is 6 by 6

Answer 2

Explanation:

Solution:

Denote the length of the rectangle as x.

The perimeter of the unit square (or rectangle) is 4

Make an equation of the area of the rectangle: (2−x)·x=0.75 ⇒ x2−2x+0.75=0 ⇒ x=0.5, x=1.5

Answer: The length will be 1.5 units