# 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?

Dec 15, 2016

See explanation.

#### Explanation:

If two figures are simmilar, the quotients of lengths of respective sides are equal to scale of similarity.

Here if the shortest side is $15$, then the scale is $k = \frac{15}{5} = 3$, so all sides of the second triangle are $3$ times longer than the respective sides of the first triangle.

So the simmilar triangle has sides of lengths: $15 , 18$ and $30$.

The longest side of the second triangle is $30$ units long.