Question

the shortest side of a triangle similar to \\( \triangle stu \\) is 40 units long.

your answer

1. determine the length of the remaining side of the similar triangle *

the shortest side of a triangle similar to \\( \triangle stu \\) is 40 units long.

Explanation:

Step1: Find the scale factor

In \(\triangle STU\), the sides are \(SU = 91\), \(ST=70\), \(UT = 98\). The shortest side of \(\triangle STU\) is \(ST = 70\). Let the scale factor \(k\) be the ratio of the shortest side of the new triangle to the shortest side of \(\triangle STU\). So \(k=\frac{40}{70}=\frac{4}{7}\)

Step2: Calculate the lengths of the other sides

For side \(SU\) (length \(91\) in \(\triangle STU\)), the length of the corresponding side in the similar triangle is \(91\times\frac{4}{7}=52\)
For side \(UT\) (length \(98\) in \(\triangle STU\)), the length of the corresponding side in the similar triangle is \(98\times\frac{4}{7} = 56\)

Answer:

The lengths of the remaining sides are \(52\) units and \(56\) units.