Question

19
the lengths of the sides of a triangle are 3 inches, 4 inches and 5 inches.
which are the side lengths of a similar triangle?
6 inches, 7 inches, 8 inches
9 inches, 12 inches, 20 inches
9 inches, 16 inches, 25 inches
6 inches, 8 inches, 10 inches

Explanation:

Step1: Recall the property of similar triangles

Similar triangles have corresponding sides in proportion.

Step2: Check each option

• Option 1: \(6,7,8\)

\(\frac{6}{3}=2\), \(\frac{7}{4} = 1.75\), \(\frac{8}{5}=1.6\). Ratios are not equal.

• Option 2: \(9,12,20\)

\(\frac{9}{3}=3\), \(\frac{12}{4} = 3\), \(\frac{20}{5}=4\). Ratios are not equal.

• Option 3: \(9,16,25\)

\(\frac{9}{3}=3\), \(\frac{16}{4} = 4\), \(\frac{25}{5}=5\). Ratios are not equal.

• Option 4: \(6,8,10\)

\(\frac{6}{3}=2\), \(\frac{8}{4} = 2\), \(\frac{10}{5}=2\). Ratios are equal.

Answer:

D. 6 inches, 8 inches, 10 inches