# 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.

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

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