Question

similar scalene triangles are drawn on a coordinate plane. one triangle has side lengths of 1, 4, and 6. the other triangle has side lengths of 3 and 12, corresponding to the first triangle. use the sss criterion to determine the third side length of the corresponding triangle. (1 point)

Explanation:

Step1: Identify the scale factor

The sides of the first triangle are 1, 4, 6. The corresponding sides of the second triangle are 3, 12, and \( x \) (let the unknown side be \( x \)). The scale factor from the first to the second triangle for the sides 1 and 3 is \( \frac{3}{1}=3 \), and for 4 and 12 is \( \frac{12}{4} = 3 \). So the scale factor is 3.

Step2: Calculate the unknown side

Using the scale factor 3, the side corresponding to 6 in the first triangle will be \( 6\times3=18 \). We can also verify using SSS similarity: \( \frac{1}{3}=\frac{4}{12}=\frac{6}{18}=\frac{1}{3} \), so the sides are proportional.

Answer:

18