Question

Sides of Similar Figures Quick Check
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Question
Three sides of a triangle measure 3, 4, and 5. Solve for the length of the shortest side of a similar triangle whose longest side has a length of 20.

Answer 1

To find the length of the shortest side of a similar triangle when the longest side is 20, we first identify the longest side of the original triangle. The sides of the triangle are 3, 4, and 5, so the longest side is 5.

Since the triangles are similar, the ratio of corresponding sides will be the same. We can set up the proportion as follows:

\[
\frac{\text{Longest side of original triangle}}{\text{Longest side of similar triangle}} = \frac{\text{Shortest side of original triangle}}{\text{Shortest side of similar triangle}}
\]

Using the given lengths:
- Longest side of the original triangle = 5
- Longest side of the similar triangle = 20
- Shortest side of the original triangle = 3

Let \( x \) be the length of the shortest side of the similar triangle. Thus, we have the proportion:

\[
\frac{5}{20} = \frac{3}{x}
\]

Now we can simplify the left side:

\[
\frac{5}{20} = \frac{1}{4}
\]

Now we set up the equation:

\[
\frac{1}{4} = \frac{3}{x}
\]

Cross-multiplying gives:

\[
1 \cdot x = 4 \cdot 3
\]

\[
x = 12
\]

Thus, the length of the shortest side of the similar triangle is **12**.