Question

10
the lengths of the sides of triangle efg are shown on the right. which one of the following triangles is similar to triangle efg? (note: the triangles are not drawn to scale.)
triangle efg: e to g is 18 in, g to f is 24 in, e to f is 27 in.
option a: triangle nom, o to m is 6 in, o to n is 8 in, n to m is 9 in.
option b: triangle nom, o to m is 4 in, o to n is 6 in, n to m is 9 in.
option c: triangle nom, o to m is 4 in, o to n is 6 in, n to m is 8 in.
option d: triangle nom, o to m is 3 in, o to n is 4 in, n to m is 8 in.

Explanation:

Step1: Simplify EFG side ratios

First, find the simplest whole-number ratio of the sides of $\triangle EFG$. The sides are 18 in, 24 in, 27 in. Divide each by their greatest common divisor (3):
$\frac{18}{3} = 6$, $\frac{24}{3} = 8$, $\frac{27}{3} = 9$
Ratio: $6:8:9$

Step2: Test Option A ratios

Sides: 6 in, 8 in, 9 in. Simplify by dividing by 1:
Ratio: $6:8:9$
This matches the ratio of $\triangle EFG$.

Step3: Verify other options (optional)

• Option B: 4 in, 6 in, 9 in. Ratio: $4:6:9$ (does not match)
• Option C: 4 in, 6 in, 8 in. Ratio: $2:3:4$ (does not match)
• Option D: 3 in, 4 in, 8 in. Ratio: $3:4:8$ (does not match)

Answer:

A. Triangle with sides 6 in, 8 in, 9 in (triangle NOM)