Question

the lengths of the sides of a triangle are 8, 15, and 17. if the longest side of a similar triangle is 51, what is the length of the shortest side?
24
4
32
16
multiple choice 4 points
the sides of \\( \triangle a b c \\) are 2,3, and 4. which set of numbers could represent the sides of a triangle similar to \\( \triangle a b c \\) ?
\\( \\{ 6,9,16 \\} \\)
\\( \\{ 12,13,14 \\} \\)
\\( \\{ 5,6,7 \\} \\)
\\( \\{ 20,30,40 \\} \\)

Explanation:

Step1: Find the ratio of sides for problem 3

The longest side of the original triangle is \(17\), and the longest side of the similar triangle is \(51\). The ratio \(r=\frac{51}{17} = 3\).

Step2: Calculate the shortest side of the similar triangle

The shortest side of the original triangle is \(8\). Using the ratio \(r = 3\), the shortest side of the similar triangle is \(8\times3=24\).

Step3: Check the ratio for problem 4

For \(\triangle ABC\) with sides \(2\), \(3\), \(4\).

• For the set \(\{20,30,40\}\), \(\frac{20}{2}=\frac{30}{3}=\frac{40}{4} = 10\).

Answer:

1. \(24\)
2. \(\{20,30,40\}\)