Question

select the correct answer.
sean has a rectangular painting with an area of 80 square inches. he wants to enlarge the painting to 320 square inches.
if the length and width of the original painting are 10 inches and 8 inches, what will the dimensions of the enlarged painting be?
a. 12 inches and 10 inches
b. 14 inches and 12 inches
c. 20 inches and 16 inches
d. 40 inches and 32 inches

Explanation:

Step1: Find the scale factor

The area of the original painting is \(80\) square inches, and the area of the enlarged painting is \(320\) square inches. The scale factor for the area is \(\frac{320}{80} = 4\). Since area scales with the square of the linear dimensions, the scale factor for the length and width is \(\sqrt{4}=2\).

Step2: Calculate the new dimensions

The original length is \(10\) inches, so the new length is \(10\times2 = 20\) inches. The original width is \(8\) inches, so the new width is \(8\times2 = 16\) inches.

Answer:

C. 20 inches and 16 inches