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.(1 point)
Responses

16
16

4
4

20
20

12

Answer 1

To solve for the length of the shortest side of a similar triangle, we can use the property that the ratios of the corresponding sides of similar triangles are equal.

The sides of the original triangle are 3 (shortest), 4, and 5 (longest). The longest side of the similar triangle is given as 20.

First, we can find the scale factor between the triangles. The longest side of the original triangle is 5, and the longest side of the similar triangle is 20:

\[ \text{Scale Factor} = \frac{\text{Longest Side of Similar Triangle}}{\text{Longest Side of Original Triangle}} = \frac{20}{5} = 4 \]

Now, we can use this scale factor to find the shortest side of the similar triangle:

The shortest side of the original triangle is 3. To find the corresponding side in the similar triangle:

\[ \text{Shortest Side of Similar Triangle} = \text{Shortest Side of Original Triangle} \times \text{Scale Factor} = 3 \times 4 = 12 \]

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