Respuesta :
Since we want to specify the length of the sides of a triangle from the known lengths of another triangle that is similar to the first one, we can express the ratios of their sides like this:
[tex]\frac{hypotenuse2}{hypotenuse1}=\frac{a2}{a1}=\frac{b2}{b1}[/tex]Where 1 means triangle 1, 2 means triangle 2, a is the first leg and b is the other leg.
Replacing the values that we know from the triangle one we get:
[tex]\begin{gathered} \frac{hypotenuse2}{hypotenuse1}=\frac{a2}{a1}=\frac{b2}{b1} \\ \frac{25}{15}=\frac{a2}{9}=\frac{b2}{12} \end{gathered}[/tex]Now, let's find the length of the second triangle with the first two ratios, like this:
[tex]\begin{gathered} \frac{25}{15}=\frac{a2}{9} \\ \frac{25}{15}\times9=\frac{a2}{9}\times9 \\ \frac{25}{15}\times9=a2 \\ a2=\frac{25}{15}\times9=\frac{5}{3}\times9=15 \end{gathered}[/tex]And for the second length of the second triangle we can use the first and the last ratio, like this:
[tex]\begin{gathered} \frac{25}{15}=\frac{b2}{12} \\ \frac{25}{15}\times12=\frac{b2}{12}\times12 \\ b2=\frac{25}{15}\times12=\frac{5}{3}\times12=20 \end{gathered}[/tex]Then the second triangle has two legs of length 15 and 20
