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

\(\displaystyle{h}^{{2}}={3}^{{2}}+{4}^{{2}}\)

\(\displaystyle{h}^{{2}}={9}+{16}\)

\(\displaystyle{h}^{{2}}={25}\)

\(\displaystyle{h}=√{25}\)

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