Question

The side length of a square is represented by x centimeters. The length of a rectangle is 3 cm greater than the side length of a square. The width of the rectangle is 3 cm less than the side length of the square. Which figure has the greater area and by how much?

Answer 1

The square has a greater area having an area of 9 cm more than that of the rectangle.

Explanation:

Length of square = x

Length of rectangle = 3+x

Width of rectangle = x-3

Area of square:

=>
`Length*Length`

=> x × x

=> x²

Area of Rectangle:

=>
`Length*Width`

=> (3+x)(x-3)

Using FOIL

=> 3x-9+x²-3x

=> x²-9

From the above calculations, we come to know that the square has a greater area having an area of 9 cm more than that of the rectangle.