Chapter 5: Q25 (page 188)

$\bar{RA}$ is an altitude of $Δ SAT$ . P and Q are midpoints of $\bar{SA}$ and $\bar{TA}$ . $SR = 9$ , $RT = 16$ , $QT = 10$ , and $PR = 7.5$ .
Find $SA$ .

Short Answer

Expert verified

$SA = 15$

Step by step solution

Step 1. Consider the diagram.

Here, $\bar{R A}$ is an altitude of $Δ S A T$ . P and Q are midpoints of $\bar{S A}$ and $\bar{T A}$ . $S R = 9$ , $R T = 16$ , $Q T = 10$ , and $P R = 7.5$ .

Step 2. Show the calculation.

Consider the triangle $Δ S A T$ .

It is given that $\bar{R A}$ is an altitude of $Δ S A T$ .

So, it can be said that the triangle $Δ A R S$ is a right triangle.

Now, $\bar{S A}$ is the hypotenuse of the right triangle $Δ A R S$ and P is its midpoint.

So, by theorem 5-15, the midpoint P of the hypotenuse $\bar{S A}$ of a right triangle $Δ A R S$ is equidistant from the three vertices.

Thus,

$S P = P R = 7.5$

Also, P is the midpoint of $\bar{S A}$ . So, it implies that,

$S P = P A$

Therefore,

$\begin{matrix} S A = S P + P A \\ = S P + S P \\ = 7.5 + 7.5 \\ = 15 \end{matrix}$

Step 3. State the conclusion.

Therefore, $S A = 15$

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$\bar{RA}$ is an altitude of $Δ SAT$ . P and Q are midpoints of $\bar{SA}$ and $\bar{TA}$ . $SR = 9$ , $RT = 16$ , $QT = 10$ , and $PR = 7.5$ .
Find $SA$ .

Short Answer

Step by step solution

Step 1. Consider the diagram.

Step 2. Show the calculation.

Step 3. State the conclusion.

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RA¯is an altitude of ΔSAT. P and Q are midpoints of SA¯and TA¯. SR=9, RT=16, QT=10, and PR=7.5.Find SA.

Short Answer

Step by step solution

Step 1. Consider the diagram.

Step 2. Show the calculation.

Step 3. State the conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Logic and Functions

Statistics

Applied Mathematics

Theoretical and Mathematical Physics

Calculus

Study anywhere. Anytime. Across all devices.

$\bar{RA}$ is an altitude of $Δ SAT$ . P and Q are midpoints of $\bar{SA}$ and $\bar{TA}$ . $SR = 9$ , $RT = 16$ , $QT = 10$ , and $PR = 7.5$ .
Find $SA$ .