Q4. - Algebra 2

Question

4. If the perimeter of $\Delta \text{PQR}$ is 3 times the length of $\text{PQ}$, then $\text{PR}=\_\_\_\_$.

 

A. 4                                  B. 6

 

C. 7                                  D. 8

Step-by-Step Solution

Answer

$PR$ is 8 and the correct option is D.

Step 1 - 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.

Step 2 - Evaluate the value of x .

From the diagram,

$PQ=6$, $QR=4$.

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

$P=PQ+QR+PR$.

Now perimeter is 3 times the length of $PQ$,

Then,

$\begin{array}{c}P=3\times PQ\\ =3\times 6\\ =18\end{array}$

Again perimeter is:

$\begin{array}{c}P=PQ+QR+PR\\ 18=6+4+x\\ 18=10+x\end{array}$

Simplify the equation using subtraction,

$\begin{array}{c}18-10=10+x-10\\ x=8\end{array}$

Thus, 

$\begin{array}{c}PR=x\\ =8\end{array}$

Step 3 - State the conclusion.

$PR$ is 8. Therefore, option D is correct.