EXAMPLE 5 Use a scale factor

In the diagram, ∆TPR ~ ∆XPZ. Find the length of the altitude PS .

SOLUTION

First, find the scale factor of ∆TPR to ∆XPZ.

TRXZ

6 + 6= 8 + 8 = 1216

= 3 4

EXAMPLE 5 Use a scale factor

Because the ratio of the lengths of the altitudes in similar triangles is equal to the scale factor, you can write the following proportion.

The length of the altitude PS is 15.

Write proportion.

Substitute 20 for PY.

Multiply each side by 20 and simplify.

PSPY

3 4=

PS20

3 4

=

=PS 15

ANSWER

GUIDED PRACTICE for Example 5

In the diagram, ABCDE ~ FGHJK.

In the diagram, ∆JKL ~ ∆ EFG. Find the length of the median KM.

7.

GUIDED PRACTICE for Example 5

JLEG

First find the scale factor of ∆ JKL to ∆ EFG.

SOLUTION

48 + 48= 40 + 40 = 96

80=

65

Because the ratio of the lengths of the median in similar triangles is equal to the scale factor, you can write the following proportion.

GUIDED PRACTICE for Example 5

SOLUTION

KM = 42

KMHF =

65

KM35

= 65

Write proportion.

Substitute 35 for HF.

Multiply each side by 35 and simplify.