Question

The smaller triangle was dilated to form the larger triangle. What is the value of x?

A smaller triangle has side lengths of 3 and 5. A larger triangle has side lengths of 9 and x + 1.

10
11
14
15

Answer 1

To solve for \( x \), we can use the property of similar triangles that states the ratios of their corresponding sides are equal.

The side lengths of the smaller triangle are 3 and 5, and the larger triangle has side lengths of 9 and \( x + 1 \).

Let's use the side lengths 3 and 9 first. We set up the ratio:

\[
\frac{3}{9} = \frac{1}{3}
\]

Now we apply the same ratio to the other pair of corresponding sides:

\[
\frac{5}{x + 1}
\]

Setting the ratios equal, we have:

\[
\frac{5}{x + 1} = \frac{1}{3}
\]

Now we can cross-multiply to solve for \( x \):

\[
5 \cdot 3 = 1 \cdot (x + 1)
\]

This simplifies to:

\[
15 = x + 1
\]

Now subtract 1 from both sides:

\[
x = 15 - 1
\]

\[
x = 14
\]

Thus, the value of \( x \) is \( \boxed{14} \).