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Chapter 5: Q25 (page 193)

In the following figure is rhombus RA炉is an altitude 螖SAT. Pand Q are midpoint of SA炉and TA炉. SR=9,RT=16,QT=10,PR=7.5. Find SA.

Short Answer

Expert verified

The value is SA=15.

Step by step solution

01

Step 1. Check the figure.

Consider the figure.

02

Step 2. Step description.

From the figure, RA炉is an altitude of 螖SAT.

Thus, 螖ARSis a right triangle.

Now, SA炉is the hypotenuse of the right triangle 螖ARSand P is the midpoint.

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

03

Step 3. Step description.

Thus, SP=PR=7.5.

Also P is the midpoint of 螖ARS, then this implies that SA=PA.

SA=SP+PASA=SP+SPSA=7.5+7.5SA=15

Therefore, the value is SA=15.

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