Question

Which of the following could be the lengths of the sides for a triangle that is similar to the triangle shown? 9,5,7

a) 10, 14, and 16
b) 8, 11.2, and 14.4
c) 7.5, 9.8, and 10.8
d) 2.5, 3, and 4.5

Answer 1

The correct set of side lengths for a triangle similar to one with sides 9, 5, and 7 is option b, consisting of side lengths 8, 11.2, and 14.4, because these maintain the same side ratio when scaled.

Step-by-step explanation:

The question asks which set of side lengths could make up a triangle similar to a given triangle with side lengths 9, 5, and 7. Since similar triangles have proportional sides, we are looking for a set of numbers with the same ratio as 9:5:7. First, we can calculate the ratios between the sides of the given triangle:

• 9/5 = 1.8
• 7/5 = 1.4
• 9/7 ≈ 1.2857

Next, let's examine the provided options:

1. Option (a) 10:14:16 does not maintain the same ratio.
2. Option (b) 8:11.2:14.4 maintains the same ratios as each side is scaled by a factor of 1.6 (8/5, 11.2/7, 14.4/9).
3. Option (c) 7.5:9.8:10.8 does not maintain the same ratio.
4. Option (d) 2.5:3:4.5 also does not maintain the same ratio.

Therefore, the correct answer is option b, as it is the only set of side lengths that maintains the same ratios and could form a triangle similar to the one with side lengths 9, 5, and 7.