Q34. Find the perimeter and area of t... [FREE SOLUTION]

91影视

Chapter 8: Q34. (page 415)

Find the perimeter and area of triangle shown below.

Short Answer

Expert verified

The perimeter of triangle is $7 \sqrt{2} + \sqrt{58} units$ .The area of given triangle is $10 square units$ .

Step by step solution

Step 1. Write down the given information.

The given triangle is shown below having coordinates $A (- 3, - 2),B (- 1, - 4) and C (4, 1)$ .

Step 2. Concept used.

If a line segment has end-points at $(x_{1}, y_{1}) and (x_{2}, y_{2})$ then the distance $(d)$ between these points is given as:

$|d| = \sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2}} . . . . (1)$

Step 3. Calculation.

The distance $(d)$ between the pair of points with given coordinates $A (- 3, - 2),B (- 1, - 4) and C (4, 1)$ is evaluated using the distance formula.

\begin{matrix} |d_{A B}| = \sqrt{{(x_{2} 鈭� x_{1})}^{2} + {(y_{2} 鈭� y_{1})}^{2}} \\ = \sqrt{{(鈭� 1 + 3)}^{2} + {(鈭� 4 + 2)}^{2}} \\ = \sqrt{8} \\ = 2 \sqrt{2} units \end{matrix}

\begin{matrix} |d_{B C}| = \sqrt{{(x_{2} 鈭� x_{1})}^{2} + {(y_{2} 鈭� y_{1})}^{2}} \\ = \sqrt{{(4 + 1)}^{2} + {(1 + 4)}^{2}} \\ = \sqrt{50} \\ = 5 \sqrt{2} units \end{matrix}

\begin{matrix} |d_{B C}| = \sqrt{{(x_{2} 鈭� x_{1})}^{2} + {(y_{2} 鈭� y_{1})}^{2}} \\ = \sqrt{{(4 + 1)}^{2} + {(1 + 4)}^{2}} \\ = \sqrt{50} \\ = 5 \sqrt{2} units \end{matrix}

Now the perimeter of triangle is the sum of its three sides. Therefore perimeter (P) of triangle (ABC) is evaluated as:

$\begin{matrix} P = |d_{A B}| + |d_{B C}| + |d_{C A}| \\ = 2 \sqrt{2} + 5 \sqrt{2} + \sqrt{58} \\ = 7 \sqrt{2} + \sqrt{58} units \end{matrix}$

And area of triangle with the given vertices $A (- 3, - 2),B (- 1, - 4) and C (4, 1)$ is evaluated as:

\begin{matrix} Area (A) = \frac{1}{2} [x_{1} (y_{2} 鈭� y_{3}) + x_{2} (y_{3} 鈭� y_{1}) + x_{3} (y_{1} 鈭� y_{2})] \\ = \frac{1}{2} [鈭� 3 (鈭� 4 鈭� 1) 鈭� 1 (1 + 2) + 4 (鈭� 2 + 4)] \\ = \frac{1}{2} [15 鈭� 3 + 8] \\ = 10 鈥媠辩耻补谤别耻苍颈迟蝉 \end{matrix}

Step 4. Conclusion.

The perimeter of triangle is $7 \sqrt{2} + \sqrt{58} units$ . The area of given triangle is $10 square units$ .

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.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

Find the perimeter and area of triangle shown below.

Short Answer

Step by step solution

Step 1. Write down the given information.

Step 2. Concept used.

Step 3. Calculation.

Step 4. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Statistics

Decision Maths

Probability and Statistics

Logic and Functions

Applied Mathematics

Study anywhere. Anytime. Across all devices.