Question

The perimeter of a square is 40m. If the area of a rectangle is 16 sq. m. less than the area of the square . Find the area of the rectangle.

Answer 1

Answer:

The usual formula for the area A of a square is given by:

(1.) A = s² , where s is the length of one of the 4 congruent sides of the square.

The formula for the perimeter P of a square is given by:

(2.) P = 4s

Now, manipulating equation (2.) in order to solve for s in terms of P, we have:

P/4 = (4s)/4

P/4 = (4/4)s

P/4 = (1)s

P/4 = s or

(3.) s = P/4

Now, substituting this result into equation (1.), we get:

A = s²

= (P/4)² , from equation (3.)

= P²/4² by a property of positive integral exponents.

(4.) A = P²/16 is the formula for the area of a square in terms of the square's perimeter.

Now, since it's given that the perimeter of a square is 40 m, then using equation (4.), we can find the square's area as follows:

A = P²/16

= (40 m)²/16

= (1600 m²)/16

= 100 m² is the final answer.

Answer 2

Area of rectangle is 84m²

Step-by-step explanation:

Perimeter of a square= 40m

Each side of square =40/4= 10m

Area of square= 10×10=100m²

Area of rectangle less than square=16 m²

Area of rectangle=100m²–16m² = 84m².