1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
bulgar [2K]
2 years ago
15

Find the area of the triangle ABC with the coordinates of A(10, 15) B(15, 15) C(30, 9).

Mathematics
1 answer:
lions [1.4K]2 years ago
6 0

Check the picture below.  so, that'd be the triangle's sides hmmm so let's use Heron's Area formula for it.

~\hfill \stackrel{\textit{\large distance between 2 points}}{d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ (\stackrel{x_1}{10}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{15}~,~\stackrel{y_2}{15}) ~\hfill a=\sqrt{[ 15- 10]^2 + [ 15- 5]^2} \\\\\\ ~\hfill \boxed{a=\sqrt{125}} \\\\\\ (\stackrel{x_1}{15}~,~\stackrel{y_1}{15})\qquad (\stackrel{x_2}{30}~,~\stackrel{y_2}{9}) ~\hfill b=\sqrt{[ 30- 15]^2 + [ 9- 15]^2} \\\\\\ ~\hfill \boxed{b=\sqrt{261}}

(\stackrel{x_1}{30}~,~\stackrel{y_1}{9})\qquad (\stackrel{x_2}{10}~,~\stackrel{y_2}{5}) ~\hfill c=\sqrt{[ 10- 30]^2 + [ 5- 9]^2} \\\\\\ ~\hfill \boxed{c=\sqrt{416}} \\\\[-0.35em] ~\dotfill

\qquad \textit{Heron's area formula} \\\\ A=\sqrt{s(s-a)(s-b)(s-c)}\qquad \begin{cases} s=\frac{a+b+c}{2}\\[-0.5em] \hrulefill\\ a=\sqrt{125}\\ b=\sqrt{261}\\ c=\sqrt{416}\\ s\approx 23.87 \end{cases} \\\\\\ A\approx\sqrt{23.87(23.87-\sqrt{125})(23.87-\sqrt{261})(23.87-\sqrt{416})}\implies \boxed{A\approx 90}

You might be interested in
Find the interest earned in an account with $600 invested at 4.5% annual simple interest for 2 years.
astra-53 [7]

Answer:

40%

Step-by-step explanation:

every year the interested be 20%

that's why in 2 years be 40%interest

3 0
3 years ago
Hannah,her dad,and her grandmother each ate 2/8. How much pizza did they eat altogether?
Vinil7 [7]

Answer:

6/8

Step-by-step explanation:

2/8 + 2/8 + 2/8 = 6/8.

Add the tops. Hope this helps :)

7 0
3 years ago
Read 2 more answers
A raindrop falls at 200m per minute. how long will it take a raindrop to travel 6000m?
Kryger [21]
The first thing you should know is that by definition:
 d = v * t
 Where
 d: distance
 v: speed
 t: time
 We then have to clear the time:
 t = (d) / (v)
 Substituting the values:
 t = (6000) / (200)
 t = 30 minutes
 Answer: 
 It will take a raindrop to travel 6000m about: 
 t = 30 minutes
5 0
3 years ago
In the given figure, identify a pair of perpendicular lines.
irakobra [83]
The answer is m and n / c
5 0
2 years ago
Read 2 more answers
These four numbers are plotted on a number line: -2/3, 5/8, -3/5, and -1/2. Which is the correct ordering on the number line fro
stiks02 [169]

Answer:

-2/3 ; - 3/5 ; - 1/2 ; 5/8

Step-by-step explanation:

Given that:

We could convert the numbers to decimal to obtain a better view of the values :

-2/3 = - 0.66666

5/8 = 0.625

-3/5 = - 0.6

-1 /2 = - 0.5

Negative values are always arranged first on left of a number line.

-0.66666 < - 0.6 < - 0.5 <0.625

Hence,

-2/3 ; - 3/5 ; - 1/2 ; 5/8

5 0
3 years ago
Other questions:
  • Help with my homework. Please.
    14·1 answer
  • The sum of the EXTERIOR angles of a pentagon equals 360°. <br> True <br> False
    5·2 answers
  • What is the volume of a cone that has a height of 7 mm and a radius of 3 mm?
    7·1 answer
  • What is 39/65 inthe lowest terms
    6·2 answers
  • Jon and Lexi are playing a marble game. According to their rules, 4 point are awarded for each red marble collected and 3 point
    6·1 answer
  • Find the vertices and foci of the hyperbola with equation quantity x plus one squared divided by sixteen minus the quantity of y
    6·2 answers
  • Two of the sides of a right triangle are 8 and 6 units long. How long is the third side? Find all possible answers. Natural leng
    12·1 answer
  • The best fruit punch requires 2/5 cup of juice concrete to 3/7 cups of water. To maintain the same taste, how many cups of water
    9·2 answers
  • A carpenter has two nails. One of the nails is 3/8 of an inch long; the other is 1/3 of an inch long. What is the difference in
    8·2 answers
  • Is what's below a complete sentence or a fragment?<br> Iris West is very happy today.
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!