Chapter 1, Problem 23RP

To determine

To calculate: The value of $RS$ .

Answer to Problem 23RP

Value of $RS$ is $14$ .

Explanation of Solution

Given information: Here, it is given that perimeter of $PRST$ is $10$ times more than $5\left(RS\right)$ and $PR=26$ . From the figure, we can conclude that $RS=PT$ and $PR=ST$ .

Formula used: Here, we are using the formula of perimeter of quadrilateral.

Perimeter of quadrilateral = Sum of all sides.

Calculation: As, it given that perimeter of $PRST$ is $10$ times more than $5(RS)$ .

  $\therefore$ Perimeter = $10+5(RS)$

Perimeter of a quadrilateral is sum of its all sides.

So, Perimeter = $PR+RS+ST+PT$

  $\Rightarrow 10+5(RS)=PR+RS+ST+PT$

Now, as it is given that $RS=PT$ and $PR=ST$ ,

  $\Rightarrow 10+5(RS)=PR+RS+PR+RS$

  $\Rightarrow 10+5(RS)=2(PR)+2(RS)$

Put value of $PR=26$ ,

  $\begin{array}{l}\begin{array}{l}\Rightarrow 10+5\left(RS\right)=2\left(26\right)+2\left(RS\right)\hfill \\ \Rightarrow 10+5\left(RS\right)=52+2\left(RS\right)\hfill \end{array}\\ \Rightarrow 5(RS)-2(RS)=52-10\\ \Rightarrow 3\left(RS\right)=42\\ \Rightarrow RS=\frac{42}{3}\\ \Rightarrow RS=14\end{array}$