Chapter 8: Q36. (page 415)

The quadrilateral RSTV has vertices $R (- 4, 6), S (4, 5), T (6, 3) and V (5, - 8)$ . Find the perimeter of quadrilateral.

Short Answer

Expert verified

The perimeter of quadrilateral is approximately $38.6 units$ .

Step by step solution

Step 1. Write down the given information.

The given quadrilateral RSTV has vertices $R (- 4, 6), S (4, 5), T (6, 3) and V (5, - 8)$ .

Step 2. Calculation.

The distance $(d)$ between the pair of points with given coordinates $R (- 4, 6), S (4, 5), T (6, 3) and V (5, - 8)$ is evaluated using the distance formula.

\begin{matrix} |d_{R S}| = \sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2}} \\ = \sqrt{{(4 + 4)}^{2} + {(5 - 6)}^{2}} \\ = \sqrt{65} units \end{matrix}

\begin{matrix} |d_{S T}| = \sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2}} \\ = \sqrt{{(6 - 4)}^{2} + {(3 - 5)}^{2}} \\ = 2 \sqrt{2} units \end{matrix}

\begin{matrix} |d_{T V}| = \sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2}} \\ = \sqrt{{(5 - 6)}^{2} + {(- 8 - 3)}^{2}} \\ = \sqrt{122} units \end{matrix}

\begin{matrix} |d_{R V}| = \sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2}} \\ = \sqrt{{(5 + 4)}^{2} + {(- 8 - 6)}^{2}} \\ = \sqrt{277} units \end{matrix}

Now the perimeter of quadrilateral is the sum of its four sides. Therefore perimeter (P) of quadrilateral (RSTV) is evaluated as:

\begin{matrix} P = |d_{R S}| + |d_{S T}| + |d_{T V}| + |d_{R V}| \\ = \sqrt{65} + 2 \sqrt{2} + \sqrt{122} + \sqrt{277} units \\ = 38.6 units (Approx.) \end{matrix}

Step 3. Conclusion.

The perimeter of quadrilateral (RSTV) is approximately $38.6 units$ .

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The quadrilateral RSTV has vertices $R (- 4, 6), S (4, 5), T (6, 3) and V (5, - 8)$ . Find the perimeter of quadrilateral.

Short Answer

Step by step solution

Step 1. Write down the given information.

Step 2. Calculation.

Step 3. Conclusion.

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The quadrilateral RSTV has vertices R-4,6,S4,5,T6,3andV5,-8. Find the perimeter of quadrilateral.

Short Answer

Step by step solution

Step 1. Write down the given information.

Step 2. Calculation.

Step 3. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Applied Mathematics

Statistics

Probability and Statistics

Mechanics Maths

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

The quadrilateral RSTV has vertices $R (- 4, 6), S (4, 5), T (6, 3) and V (5, - 8)$ . Find the perimeter of quadrilateral.