The areas of two similar triangles are 25 cm² and 64 cm². An altitude of the smaller triangle is 10 cm. What is the matching altitude of the larger triangle?

6.25 cmCorrect answerYour answer13 cmCorrect answerYour answer16 cmCorrect answerYour answer25.6 cmCorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

Ratio of areas = $25 : 64$ , so the ratio of matching lengths = $\sqrt{25} : \sqrt{64} = 5 : 8$ .
Larger altitude = $10 \times \frac{8}{5} = 16$ cm.

Worth noting

25.6 cm uses the area ratio directly on a length. Altitudes, medians and sides all scale by the square root of the area ratio.

Concept: Lengths in similar triangles scale by the square root of the area ratio
Typical timeTypical: 70 s
Your timeYours: —

Ten questions from Lines, Triangles and Circles, at your own pace.

Explanation