Chapter 1: Q4. (page 52)

4. If the perimeter of $Δ PQR$ is 3 times the length of $PQ$ , then $PR =____$ .
A. 4 B. 6
C. 7 D. 8

Short Answer

Expert verified

$P R$ is 8 and the correct option isD.

Step by step solution

- State the definition of a variable.

A variable is a term that is used to represent an unknown value.

Here, let x be the length of PR.

- Evaluate the value of x.

From the diagram,

$P Q = 6$ , $Q R = 4$ .

The perimeter (P) of triangle is sum of the three sides that is:

$P = P Q + Q R + P R$ .

Now perimeter is 3 times the length of $P Q$ ,

Then,

\begin{matrix} P = 3 \times P Q \\ = 3 \times 6 \\ = 18 \end{matrix}

Again perimeter is:

\begin{matrix} P = P Q + Q R + P R \\ 18 = 6 + 4 + x \\ 18 = 10 + x \end{matrix}

Simplify the equation using subtraction,

\begin{matrix} 18 - 10 = 10 + x - 10 \\ x = 8 \end{matrix}

Thus,

\begin{matrix} P R = x \\ = 8 \end{matrix}

- State the conclusion.

$P R$ is 8. Therefore, option D is correct.

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4. If the perimeter of $Δ PQR$ is 3 times the length of $PQ$ , then $PR =____$ .
A. 4 B. 6
C. 7 D. 8

Short Answer

Step by step solution

- State the definition of a variable.

- Evaluate the value of x.

- State the conclusion.

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4. If the perimeter of ΔPQRis 3 times the length of PQ, then PR=____.A. 4 B. 6C. 7 D. 8

Short Answer

Step by step solution

- State the definition of a variable.

- Evaluate the value of x.

- State the conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Discrete Mathematics

Calculus

Pure Maths

Logic and Functions

Mechanics Maths

Study anywhere. Anytime. Across all devices.

4. If the perimeter of $Δ PQR$ is 3 times the length of $PQ$ , then $PR =____$ .
A. 4 B. 6
C. 7 D. 8