Chapter 5: Q26 (page 188)

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

Short Answer

Expert verified

The perimeter of $Δ PQR = 30$ .

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.

By definition of altitude,

$\bar{R A} ⊥ \bar{S T}$

The midpoint of the hypotenuse of the right triangle is equidistant from the three vertices.

In $Δ A R T$ , Q is the midpoint of $\bar{T A}$ .

So,

$A Q = R Q = Q T$

Hence,

$R Q = 10$

In $Δ A S T$ , P and Q are midpoints of sides $\bar{A S}$ and $\bar{A T}$ and $\bar{S T}$ is the third side.

So,

$P Q = \frac{1}{2} S T$

From segment addition postulate,

$\begin{matrix} S T = S R + R T \\ = 9 + 16 \\ = 25 \end{matrix}$

Hence,

$\begin{matrix} P Q = \frac{25}{2} \\ = 12.5 \end{matrix}$

In $Δ P Q R$ ,

Perimeter is:

$\begin{matrix} Perimeter = P Q + Q R + P R \\ = 12.5 + 10 + 7.5 \\ = 30 \end{matrix}$

Step 3. State the conclusion.

Therefore, perimeter is 30.

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

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

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

Mechanics Maths

Logic and Functions

Probability and Statistics

Calculus

Statistics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

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

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

Mechanics Maths

Logic and Functions

Probability and Statistics

Calculus

Statistics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

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