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

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.