Question

Triangles DEF and HJK are similar. DEF has side lengths DE=4, EF=6, FD=8. Which of the following could be the side lengths of HJK?• 2, 6, 7• 2, 5, 7• 8, 12, 16• 5, 7, 9

Answer 1

(c) 8, 12, 16

Explanation:

You want to identify the side lengths that are proportional to lengths 4, 6, and 8.

Ratios

Reducing the ratios to lowest terms, we can compare them:

• desired ratio: 4 : 6 : 8 = 2 : 3 : 4
• 2 : 6 : 7 — reduced, not equivalent
• 2 : 5 : 7 — reduced, not equivalent
• 8 : 12 : 16 = 2 : 3 : 4 . . . . . same as the desired ratios
• 5 : 7 : 9 — reduced, not equivalent

Side lengths 8, 12, 16 will form a triangle similar to ∆DEF.

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