Question

if the side lengths are tripled, then which of the following is true? the new area will be 9 times the old area. the new area will be 4 times the old area. the new area will be 3 times the old area.

Explanation:

Step1: Recall area - side relationship

Let the original side - length of a square (assuming it's a square as the problem involves side - length and area change) be $s$, and the original area $A = s^2$.

Step2: Calculate new side - length and area

If the side - length is tripled, the new side - length $s_{new}=3s$. Then the new area $A_{new}=(3s)^2 = 9s^2$.

Step3: Compare new and old areas

Since $A_{new}=9s^2$ and $A = s^2$, the new area is 9 times the old area.

Answer:

The new area will be 9 times the old area.