Question

If a figure has one dimension of 4 inches and an area of 20 square inches, what is the measure of the corresponding part in a similar figure 3 times as big?

Answer 1

what is the area of the second figure

Answer 2

To determine the corresponding measure in a similar figure that is 3 times as big, we first need to figure out what the missing dimension of the original figure is.

We know that for a shape that has an area of 20 square inches and one dimension of 4 inches, we can find the other dimension by using the formula for the area of a rectangle (if we assume that the figure is rectangular, as it is a common interpretation):

\[
\text{Area} = \text{length} \times \text{width}
\]

Let \(w\) be the unknown dimension. We have:

\[
20 = 4 \times w
\]

To solve for \(w\):

\[
w = \frac{20}{4} = 5 \text{ inches}
\]

Now we know the dimensions of the original figure are 4 inches and 5 inches.

Since the similar figure is 3 times as big, we multiply each dimension by 3:

The dimensions of the larger figure will be:

\[
4 \text{ inches} \times 3 = 12 \text{ inches}
\]

\[
5 \text{ inches} \times 3 = 15 \text{ inches}
\]

Therefore, the corresponding part in the similar figure that is 3 times as big is:

**12 inches** for the dimension initially measuring 4 inches, and **15 inches** for the dimension initially measuring 5 inches.

Answer 3

To find the area of the second figure, which has dimensions that are 3 times larger than those of the original figure, we already established the dimensions of the larger figure:

- The first dimension is \(12\) inches (3 times \(4\) inches).
- The second dimension is \(15\) inches (3 times \(5\) inches).

Now, we can calculate the area of the second figure using the formula for the area of a rectangle:

\[
\text{Area} = \text{length} \times \text{width}
\]

Substituting in the dimensions of the larger figure:

\[
\text{Area} = 12 \text{ inches} \times 15 \text{ inches} = 180 \text{ square inches}
\]

Thus, the area of the second figure is **180 square inches**.