Find the unknown side length labeled with a variable in the given pair of similar triangles. 27 18 33 *** Se X = (Simplify your answer.)
Find the unknown side length labeled with a variable in the given pair of similar triangles. 27 18 33 *** Se X = (Simplify your answer.)
ChapterP: Prerequisites
SectionP.6: The Rectangular Coordinate System And Graphs
Problem 37E: An airplane flies from Naples, Italy, in a straight line to Rome, Italy, which is 120 kilometers...
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![**Find the unknown side length labeled with a variable in the given pair of similar triangles.**
*[Image Description]*
The image displays two right triangles that are similar to each other. In the smaller triangle, the two legs of the right triangle have lengths of 18 and 27. In the larger triangle, one of the legs has a length of 33, and the length of the other leg is labeled as \( x \).
To determine the length of the unknown side \( x \), notice that both pairs of triangles are similar, meaning the corresponding side lengths are proportional. We can set up a proportion to solve for \( x \):
\[
\text{(leg1 for small triangle)} / \text{(leg2 for small triangle)} = \text{(leg1 for large triangle)} / \text{(leg2 for large triangle)}
\]
Given:
\[
18 / 27 = x / 33
\]
Simplifying the proportion:
\[
\frac{18}{27} = \frac{2}{3}
\]
Setting up the equation:
\[
\frac{2}{3} = \frac{x}{33}
\]
Solving for \( x \):
\[
2 * 33 = 3 * x
\]
\[
66 = 3x
\]
\[
x = \frac{66}{3}
\]
\[
x = 22
\]
Therefore,
\[
x = \boxed{22}
\]
(Simplify your answer.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9c3214b5-f2f5-4a89-904a-2906edf42c76%2Fc26cc5aa-dcc1-49e9-b115-ecec9d9583e4%2Fw18jix1_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Find the unknown side length labeled with a variable in the given pair of similar triangles.**
*[Image Description]*
The image displays two right triangles that are similar to each other. In the smaller triangle, the two legs of the right triangle have lengths of 18 and 27. In the larger triangle, one of the legs has a length of 33, and the length of the other leg is labeled as \( x \).
To determine the length of the unknown side \( x \), notice that both pairs of triangles are similar, meaning the corresponding side lengths are proportional. We can set up a proportion to solve for \( x \):
\[
\text{(leg1 for small triangle)} / \text{(leg2 for small triangle)} = \text{(leg1 for large triangle)} / \text{(leg2 for large triangle)}
\]
Given:
\[
18 / 27 = x / 33
\]
Simplifying the proportion:
\[
\frac{18}{27} = \frac{2}{3}
\]
Setting up the equation:
\[
\frac{2}{3} = \frac{x}{33}
\]
Solving for \( x \):
\[
2 * 33 = 3 * x
\]
\[
66 = 3x
\]
\[
x = \frac{66}{3}
\]
\[
x = 22
\]
Therefore,
\[
x = \boxed{22}
\]
(Simplify your answer.)
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