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Chapter 5: Q27 (page 188)

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

Find the perimeter of 螖SAT.

Short Answer

Expert verified

The perimeter of 螖SAT=60.

Step by step solution

01

Step 1. Consider the diagram.

Here, 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.

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,

AQ=RQ=10

From the segment addition postulate,

AQ+QT=ATAT=10+10=20

In 螖ARS, Pis the midpoint of SA炉.

SP=PA=PRSP=PA=7.5

From the segment addition postulate,

SP+PA=SASA=7.5+7.5=15

From the segment addition postulate,

ST=SR+RT=9+16=25

In 螖AST,

Perimeter is:

Perimeter=AS+ST+AT=15+25+20=60

03

Step 3. State the conclusion.

Therefore, the perimeter is 60.

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