Question

Assume the following triangles are similar. Find the scale factor and the lengths of the missing sides.

Answer 1

Answer:

If two figures are similar, then the correspondent sides are related by a constant factor.

For example, if the base of one side of one of the figures has a length L, then the correspondent side of the other figure has a length k*L where k is the scale factor.

Let's start with the two left triangles.

In the smaller one the base is 5, and the base of the other triangle is 15.

Then we will have:

15 = k*5

15/5 = k = 3

The scale factor is 3.

Then we will have that:

a = scale factor times the correspondent side in the smaller triangle:

a = k*3 = 3*3 = 9

a = 9

For the other two triangles, the base of the smaller triangle is 12, while the base of the larger triangle is 20.

Then we will have the relation:

12*k = 20

k = (20/12) = 10/6 = 5/3

The scale factor is 5/3

This means that the unknown side b is given by:

b*(5/3) = 15

b = (3/5)*15 = 3*3 = 9

b = 9.