Question

Four identical rectangles surround a square. The perimeter of each rectangle is 20 cm and the area of the square is 44 cm². What is the area of each rectangle?

Answer 1

Let x be the length of one side of the square. Then, the perimeter of the square is 4x.

Each rectangle has two sides that are equal in length to the side of the square, and two sides that are equal in length to some other value y. Therefore, the perimeter of each rectangle can be expressed as:

2x + 2y = 20

Simplifying this equation, we get:

x + y = 10

We can use this relationship to solve for y in terms of x:

y = 10 - x

The area of each rectangle is given by:

Area = x*y

Substituting y = 10 - x, we get:

Area = x*(10-x)

Area = 10x - x²

To find the area of each rectangle, we need to solve for x. We know that the area of the square is 44 cm², so:

x² = 44

x ≈ 6.63 cm

Now we can find the area of each rectangle:

Area = 10x - x²

Area = 10(6.63) - (6.63)²

Area ≈ 38.85 cm²

Therefore, each rectangle has an area of approximately 38.85 cm².