Question

look at this triangle: if all three dimensions are quadrupled, then which of the following statements about its perimeter will be true? the new perimeter will be 3 times the old perimeter. the new perimeter will be 1/2 of the old perimeter. the new perimeter will be 2 times the old perimeter. the new perimeter will be 4 times the old perimeter.

Explanation:

Step1: Calculate the original perimeter

The original triangle has side - lengths 5 yd, 7 yd, and 9 yd. The perimeter $P_{1}$ of a triangle is the sum of its side - lengths. So, $P_{1}=5 + 7+9=21$ yd.

Step2: Calculate the new side - lengths after quadrupling

If each side - length is quadrupled, the new side - lengths are $5\times4 = 20$ yd, $7\times4 = 28$ yd, and $9\times4 = 36$ yd.

Step3: Calculate the new perimeter

The new perimeter $P_{2}$ is $P_{2}=20 + 28+36=84$ yd.

Step4: Compare the new and old perimeters

We find the ratio of the new perimeter to the old perimeter: $\frac{P_{2}}{P_{1}}=\frac{84}{21}=4$. So the new perimeter is 4 times the old perimeter.

Answer:

The new perimeter will be 4 times the old perimeter.