Question

The sides of a triangle are $5,6$ and $10$.

How do you find the length of the longest side of a similar triangle whose shortest side is $15$?

Answer 1

Use the similarity of triangles to find the length of unknown side:

We know that the corresponding sides of the similar triangles are in the same ratio.

It is given that the length of shortest and longest of first triangle are $5$ and $10$ respectively, and the length of shortest side of other triangle is $15$

Let the length of the longest side of the other triangle be $\mathrm{x}$

Then, the ratio of corresponding sides is,

$\frac{5}{15}=\frac{10}{\mathrm{x}}$

$\Rightarrow$$\frac{1}{3}=\frac{10}{\mathrm{x}}$

$\Rightarrow$ $\mathrm{x}=10\times 3$

$\Rightarrow$ $\mathrm{x}=30$

Hence, the length of the longest side of the other triangle is $30$.