Question

The outer rectangle is shaded. The outer rectangle's length is 2x+2 and the width is 3x-4. The inside rectangle's length is x-3 and the width is x-6. What is the area of the outer rectangle?

Answer 1

Thank you

Answer 2

To find the area of the outer rectangle, we need to multiply its length by its width.

Length of outer rectangle = 2x+2
Width of outer rectangle = 3x-4

Area of outer rectangle = (2x+2) * (3x-4)

Now, we need to subtract the area of the inner rectangle from the area of the outer rectangle to find the shaded area.

Length of inner rectangle = x-3
Width of inner rectangle = x-6

Area of inner rectangle = (x-3) * (x-6)

Shaded area = Area of outer rectangle - Area of inner rectangle

Shaded area = (2x+2) * (3x-4) - (x-3) * (x-6)

Simplifying this expression, we get:

Shaded area = 5x^2 - 16x + 18

Therefore, the area of the outer rectangle is 5x^2 - 16x + 18.