MATH SOLVE

5 months ago

Q:
# 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. 10B.20C. 40D. 80with explanation

Accepted Solution

A:

Answer:C) The area of the landscape model is A = 40 sq ft.Step-by-step explanation:The original dimensions of the rectangular patio model isLength = LWidth = WArea 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 ABut, the area of the new enlarged patio is 160 square feet.⇒ 160 sq ft = 4 x Aor, A = 160 / 4 =40 sq ft⇒ A = 40 sq ft.Hence, the area of the landscape model is A = 40 sq ft.