Chapter 5: Q25 (page 193)

In the following figure is rhombus $\bar{R A}$ is an altitude $Δ S A T$ . Pand Q are midpoint of $\bar{S A}$ and $\bar{T A}$ . $S R = 9, R T = 16, Q T = 10, P R = 7.5$ . Find $S A$ .

Short Answer

Expert verified

The value is $S A = 15$ .

Step by step solution

Step 1. Check the figure.

Consider the figure.

Step 2. Step description.

From the figure, $\bar{R A}$ is an altitude of $Δ S A T$ .

Thus, $Δ A R S$ is a right triangle.

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

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

Step 3. Step description.

Thus, $S P = P R = 7.5$ .

Also P is the midpoint of $Δ A R S$ , then this implies that $S A = P A$ .

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

Therefore, the value is $S A = 15$ .

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In the following figure is rhombus $\bar{R A}$ is an altitude $Δ S A T$ . Pand Q are midpoint of $\bar{S A}$ and $\bar{T A}$ . $S R = 9, R T = 16, Q T = 10, P R = 7.5$ . Find $S A$ .

Short Answer

Step by step solution

Step 1. Check the figure.

Step 2. Step description.

Step 3. Step description.

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

Short Answer

Step by step solution

Step 1. Check the figure.

Step 2. Step description.

Step 3. Step description.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Theoretical and Mathematical Physics

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Statistics

Probability and Statistics

Study anywhere. Anytime. Across all devices.

In the following figure is rhombus $\bar{R A}$ is an altitude $Δ S A T$ . Pand Q are midpoint of $\bar{S A}$ and $\bar{T A}$ . $S R = 9, R T = 16, Q T = 10, P R = 7.5$ . Find $S A$ .