Question

I need help!!!
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

Answer 1

Answer: OPTION C.

Step-by-step explanation:

1. By defintion the scale factor of the area is $k^{2}$ and this is:

$k^{2}=\frac{A_1}{A_2}=\frac{320}{80}=4$

2. Then, the scale factor for the sides is:

$k=\sqrt{4}=2$

3. Now, you must multiply the length and the width of the original rectangle by 2 to obtain the new dimensions. Thefore, you obtain:

$l=10in*2=20in\\w=8in*2=16in$

Therefore, the answer is the option C.