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 $A_1 = 10\times8=80$ square inches. The area of the enlarged painting is $A_2 = 320$ square inches. Let the scale - factor be $k$. Since the ratio of the areas of two similar rectangles is equal to the square of the scale - factor, $\frac{A_2}{A_1}=k^{2}$. So, $k^{2}=\frac{320}{80}=4$, then $k = 2$.

Step2: Calculate the new dimensions

The original length is $l_1 = 10$ inches and the original width is $w_1 = 8$ inches. The new length $l_2=k\times l_1=2\times10 = 20$ inches, and the new width $w_2=k\times w_1=2\times8 = 16$ inches.

Answer:

C. 20 inches and 16 inches