Similar Triangles: Calculate Perimeter Using 12-13-5 Triangle Measurements

Question

The triangle above are similar.

What is the perimeter of the blue triangle?

00:00 Find the perimeter of the triangle according to the similarity ratio

00:03 The perimeter of the triangle equals the sum of its sides

00:09 This is the known triangle perimeter

00:15 The perimeter of the triangles equals the similarity ratio

00:23 Let's substitute appropriate values and solve for the perimeter

00:34 Multiply by the reciprocal to isolate P

00:45 And this is the solution to the question

The perimeter of the left triangle: 13+12+5=25+5=30

Therefore, the perimeter of the right triangle divided by 30 is equal to 5.2 divided by 13:

$\frac{x}{30}=\frac{5.2}{13}$

$13x=156$

$x=12$