Question

A model of a rectangular patio at a landscaping business will be enlarged by a scale factor of 2 when it is installed in a customer’s back yard. The area of the new enlarged patio will be 160 square feet. Which is the area of the landscaper’s model?

A. 10
B.20
C. 40
D. 80

with explanation

Answer 1

ITSSS.... 40

Explanation:

Answer 2

C) The area of the landscape model is A = 40 sq ft.

Explanation:

The original dimensions of the rectangular patio model is

Length = L

Width = W

Area of the patio model = LENGTH x WIDTH = L x W

⇒ A = L W ............. (1)

Now, the new area A" is enlarged by a factor of 2

⇒ The new Length = L" = (2 L)

The new Width = W" = (2 W)

So, AREA" = L" x W" = (2 L) x (2 W) = 4 (L W)

⇒ A " = 4 (L W)

But, L W = A .. from (1)

⇒ A" = 4 A

But, the area of the new enlarged patio is 160 square feet.

⇒ 160 sq ft = 4 x A

or, A = 160 / 4 =40 sq ft

⇒ A = 40 sq ft.

Hence, the area of the landscape model is A = 40 sq ft.