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Chapter 5: Q25 (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 SA.

Short Answer

Expert verified

SA=15

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.

Consider the triangle 螖SAT.

It is given that RA炉is an altitude of 螖SAT.

So, it can be said that the triangle 螖ARSis a right triangle.

Now, SA炉 is the hypotenuse of the right triangle 螖ARS and P is its midpoint.

So, by theorem 5-15, the midpoint P of the hypotenuse SA炉of a right triangle 螖ARSis equidistant from the three vertices.

Thus,

SP=PR=7.5

Also, P is the midpoint of SA炉. So, it implies that,

SP=PA

Therefore,

SA=SP+PA=SP+SP=7.5+7.5=15

03

Step 3. State the conclusion.

Therefore, SA=15

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