Two right triangles are similar. The legs of the smaller triangle have lengths of 3 and 4. The scale factor is 1:3. Find the length of the hypotenuse of the larger triangle.

Two right triangles are similar. The legs of the smaller triangle have lengths of 3 and 4. The scale factor is 1:3. Find the length of the hypotenuse of the larger triangle.

Question
Two right triangles are similar. The legs of the smaller triangle have lengths of 3 and 4. The scale factor is 1:3. Find the length of the hypotenuse of the larger triangle.

Answers (1)

2021-02-01
Using the smaller triangle, we find its hypotenuse, hh, usingh Pythagorean Theorem:
\(\displaystyle{h}^{{2}}={3}^{{2}}+{4}^{{2}}\)
\(\displaystyle{h}^{{2}}={9}+{16}\)
\(\displaystyle{h}^{{2}}={25}\)
\(\displaystyle{h}=√{25}\)
h=5
Let x be the hypotenuse of the larger triangle. Using the scale factor, we can write the propotion:
\(\displaystyle\frac{{1}}{{3}}=\frac{{h}}{{x}}\)
\(\displaystyle\frac{{1}}{{3}}=\frac{{5}}{{x}}\)
x=3(5)
x=15
0

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