Question

look at this square: if the side lengths are tripled, then which of the following statements about its area will be true? the ratio of the new area to the old area will be 3:1. the ratio of the new area to the old area will be 9:1. the ratio of the new area to the old area will be 27:1. the ratio of the new area to the old area will be 4:1.

Explanation:

Step1: Recall area formula for square

The area formula of a square is $A = s^2$, where $s$ is the side - length. Let the original side - length be $s_1$ and the new side - length be $s_2$.

Step2: Determine relationship between side - lengths

Given that the side - lengths are tripled, so $s_2=3s_1$.

Step3: Calculate original and new areas

The original area $A_1 = s_1^2$, and the new area $A_2=s_2^2=(3s_1)^2 = 9s_1^2$.

Step4: Find the ratio of new area to old area

The ratio $\frac{A_2}{A_1}=\frac{9s_1^2}{s_1^2}=9:1$.

Answer:

The ratio of the new area to the old area will be 9:1.