Question

In the diagram, the smaller square has a side length of 3 centimeters, and the larger square has a side length of 24 centimeters. Calculate and compare the perimeters of the similar squares. What is the ratio of the small square to the larger square? Enter you response as a fraction.

Answer 1

To calculate the perimeters of the smaller and larger squares, we use the formula for the perimeter of a square, which is:

\[
\text{Perimeter} = 4 \times \text{side length}
\]

**Step 1: Calculate the perimeter of the smaller square.**

For the smaller square with a side length of 3 centimeters:

\[
\text{Perimeter}_{\text{small}} = 4 \times 3 = 12 \text{ cm}
\]

**Step 2: Calculate the perimeter of the larger square.**

For the larger square with a side length of 24 centimeters:

\[
\text{Perimeter}_{\text{large}} = 4 \times 24 = 96 \text{ cm}
\]

**Step 3: Calculate the ratio of the perimeters of the smaller square to the larger square.**

The ratio of the perimeter of the smaller square to the larger square is:

\[
\text{Ratio} = \frac{\text{Perimeter}_{\text{small}}}{\text{Perimeter}_{\text{large}}} = \frac{12}{96}
\]

**Step 4: Simplify the ratio.**

To simplify \(\frac{12}{96}\):

\[
\frac{12 \div 12}{96 \div 12} = \frac{1}{8}
\]

Thus, the ratio of the perimeters of the smaller square to the larger square is:

\[
\boxed{\frac{1}{8}}
\]