Answer:
One similar triangle: 15, 36 and 39
Another similar triangle: 10, 24, 26
Explanation:
When a triangle is similar, it has corresponding sides that are each longer are shorter than the original triangle by a scale factor.
Scale factor
A scale factor is a number that you multiply the original triangle's sides by. After multiplying each original side, you get the side lengths of a new and similar triangle.
The original sides from the question are 5, 12 and 13.
First similar triangle
Let's pick 3 to be a scale factor.
Multiply every original side by the scale factor to get the side lengths of a similar triangle.
5 × 3 = 15
12 × 3 = 36
13 × 3 = 39
∴ One similar triangle can have the sides 15, 36 and 39.
Second similar triangle
Let's pick another scale factor: 2
Now, we do the same. Multiply the original sides by the scale factor.
5 × 2 = 10
12 × 2 = 24
13 × 2 = 26
∴ Another similar triangle can have the sides 10, 24 and 26.
Choosing a scale factor
We can pick almost any number to be a scale factor. If we pick a scale factor that is:
- greater than 1, then the similar triangle will be larger.
- a fraction, then the similar triangle will be smaller.
We can make an infinite amount of other similar triangles just by changing the scale factor.