The question in the image asks:

"If both dimensions are quadrupled, then which of the following statements about its perimeter will be true?"

The rectangle shown has dimensions 6 m by 9 m. If both dimensions are quadrupled, the new dimensions would be:

• New length: $6 \times 4 = 24$ m
• New width: $9 \times 4 = 36$ m

The perimeter $P$ of a rectangle is calculated using the formula: $P = 2 \times (\text{length} + \text{width})$

Old perimeter: $P_{\text{old}} = 2 \times (6 + 9) = 2 \times 15 = 30 \text{ meters}$

New perimeter: $P_{\text{new}} = 2 \times (24 + 36) = 2 \times 60 = 120 \text{ meters}$

Now, to compare the new perimeter with the old: $\frac{P_{\text{new}}}{P_{\text{old}}} = \frac{120}{30} = 4$ So, the new perimeter is 4 times the old perimeter.

The correct answer is: "The new perimeter will be 4 times the old perimeter."

Would you like any further details or have any questions?

Here are 5 related questions to think about:

1. What happens to the area of the rectangle when both dimensions are quadrupled?
2. How would the perimeter change if the dimensions were doubled instead of quadrupled?
3. If only one dimension is quadrupled, what happens to the perimeter?
4. How would the area change if only one dimension is quadrupled?
5. How do changes in scale affect the ratio of the new area to the old area?

Tip: Remember that the perimeter scales linearly with dimension changes, while the area scales quadratically!