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Chapter 5: Q26 (page 188)

RA炉is an altitude of 螖SAT. Pand Q are midpoints of SA炉and TA炉. SR=9, RT=16, QT=10, and PR=7.5.

Find the perimeter of 螖PQR.

Short Answer

Expert verified

The perimeter of 螖PQR=30.

Step by step solution

01

Step 1. Consider the diagram.

Here, RA炉is an altitude of 螖SAT. P and Q are midpoints of SA炉and TA炉. SR=9, RT=16, QT=10, and PR=7.5.

02

Step 2. Show the calculation.

By definition of altitude,

RA炉鈯�ST炉

The midpoint of the hypotenuse of the right triangle is equidistant from the three vertices.

In 螖ART, Q is the midpoint of TA炉.

So,

AQ=RQ=QT

Hence,

RQ=10

In 螖AST, P and Q are midpoints of sides AS炉and AT炉and ST炉is the third side.

So,

PQ=12ST

From segment addition postulate,

ST=SR+RT=9+16=25

Hence,

PQ=252=12.5

In 螖PQR,

Perimeter is:

Perimeter=PQ+QR+PR=12.5+10+7.5=30

03

Step 3. State the conclusion.

Therefore, perimeter is 30.

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