Question

The side length of the four sided square is 3 cm, the side length is tripled

Which percent of increase is greater: the percent of increase for the perimeter of the square or the percent of increase for the area? How much greater?

The percent increase for the (?) is greater

It is (?)% greater.

Answer 1

Let's start by calculating the perimeter and area of the original square with a side length of 3 cm.

1. **Original square**:
- Side length = 3 cm
- Perimeter = \(4 \times \text{side length} = 4 \times 3 = 12\) cm
- Area = \(\text{side length}^2 = 3^2 = 9\) cm²

When the side length is tripled:

2. **New side length**:
- New side length = \(3 \times 3 = 9\) cm

3. **New square**:
- New perimeter = \(4 \times 9 = 36\) cm
- New area = \(9^2 = 81\) cm²

Next, we'll calculate the percent increase for the perimeter and the area.

4. **Percent increase for the perimeter**:
\[
\text{Percent increase} = \left( \frac{\text{New perimeter} - \text{Original perimeter}}{\text{Original perimeter}} \right) \times 100
\]
\[
= \left( \frac{36 - 12}{12} \right) \times 100 = \left( \frac{24}{12} \right) \times 100 = 2 \times 100 = 200\%
\]

5. **Percent increase for the area**:
\[
\text{Percent increase} = \left( \frac{\text{New area} - \text{Original area}}{\text{Original area}} \right) \times 100
\]
\[
= \left( \frac{81 - 9}{9} \right) \times 100 = \left( \frac{72}{9} \right) \times 100 = 8 \times 100 = 800\%
\]

Now, we can compare the percent increases:

- Percent increase for the perimeter: **200%**
- Percent increase for the area: **800%**

To determine which percent increase is greater and by how much:

- The percent increase for the area is greater than the percent increase for the perimeter by:
\[
800\% - 200\% = 600\%
\]

### Conclusion:
The percent increase for the **area** is greater. It is **600%** greater.