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
Eddi Din [679]
3 years ago
5

The vertices of ∆ABC are A(-2, 2), B(6, 2), and C(0, 8). The perimeter of ∆ABC is units is? What is the area?

Mathematics
2 answers:
11111nata11111 [884]3 years ago
4 0

we have

A(-2, 2),B(6, 2),C(0, 8)

see the attached figure to better understand the problem

we know that

The perimeter of the triangle is equal to

P=AB+BC+AC

and

the area of the triangle is equal to

A=\frac{1}{2}*base *heigth

in this problem

base=AB\\heigth=DC

we know that

The distance between two points is equal to

d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}

Step 1

<u>Find the distance AB</u>

A(-2, 2),B(6, 2)

Substitute the values in the formula

d=\sqrt{(2-2)^{2}+(6+2)^{2}}

d=\sqrt{(0)^{2}+(8)^{2}}

dAB=8\ units

Step 2

<u>Find the distance BC</u>

B(6, 2),C(0, 8)

Substitute the values in the formula

d=\sqrt{(8-2)^{2}+(0-6)^{2}}

d=\sqrt{(6)^{2}+(-6)^{2}}

dBC=6\sqrt{2}\ units

Step 3

<u>Find the distance AC</u>

A(-2, 2),C(0, 8)

Substitute the values in the formula

d=\sqrt{(8-2)^{2}+(0+2)^{2}}

d=\sqrt{(6)^{2}+(2)^{2}}

dAC=2\sqrt{10}\ units

Step 4

<u>Find the distance DC</u>

D(0, 2),C(0, 8)

Substitute the values in the formula

d=\sqrt{(8-2)^{2}+(0-0)^{2}}

d=\sqrt{(6)^{2}+(0)^{2}}

dDC=6\ units

Step 5

<u>Find the perimeter of the triangle</u>

P=AB+BC+AC

substitute the values

P=8\ units+6\sqrt{2}\ units+2\sqrt{10}\ units

P=22.81\ units

therefore

The perimeter of the triangle is equal to 22.81\ units

Step 6

<u>Find the area of the triangle</u>

A=\frac{1}{2}*base *heigth

in this problem

base=AB=8\ units\\heigth=DC=6\ units

substitute the values

A=\frac{1}{2}*8*6

A=24\ units^{2}

therefore

the area of the triangle is 24\ units^{2}

malfutka [58]3 years ago
3 0
Best is to draw a sketch of the three points.
Next step is to find the distances BC, CD, DB.
The perimeter is the sum of the three distances.

The distances are found using the distance formula:
D=sqrt((y2-y1)^2+(x2-x1)^2)
<span>order of (x1,y1), (x2,y2) is not important.

Given A(2,8),B(16,2),C(6,2)
we calculate 
AB=sqrt((16-2)^2+(2-8)^2)=sqrt(14^2+6^2)=sqrt(232);
BC=sqrt((6-16)^2+(2-2)^2)=sqrt(10^2+0)=10
CA=sqrt((2-6)^2+(8-2)^2)=sqrt(4^2+6^2)=sqrt(16+36)=sqrt(52)

Perimeter=AB+BC+CA=32.443 units

For the area, we note that BC is horizontal (parallel to the x-axis), so 
area = (1/2)bast * height
=(1/2)10*(ya-yb)
=(1/2)10*(8-2)
=(1/2)10*6
=30 unit^2</span>
You might be interested in
Use the interactive number line to find each sum to complete the table
Likurg_2 [28]

-1 - 2 = -3

R = -3

-4 + 1 = -3

S = -3

-6 - 3 = -9

T = -9

6 0
2 years ago
Read 2 more answers
Find the equation whose graph is shown below. Write your answer in standard form.
vladimir2022 [97]

Answer:

it as a liner function that is why we should choose to point in order to find the liner equation

y=2/3x+1

5 0
2 years ago
1/3+2/3m=2/3m-2/3<br><br> Does it have no solution or is it an identity?
Crazy boy [7]
\dfrac{1}{3}+\dfrac{2}{3}m=\dfrac{2}{3}m-\dfrac{2}{3}\ \ \ \ \ |subtract\ \dfrac{2}{3}m\ from\ both\ sides\\\\\dfrac{1}{3}=-\dfrac{2}{3}\ \ \ \ FALSE\\\\Answer:\ No\ solution
3 0
3 years ago
Can someone please help me work out the area​
irga5000 [103]

Answer:

just use the formula length×width×height

Step-by-step explanation:

1 cube= 1cm

length=4x1cm

width=2x1cm

height=4x1cm

add together

4x4x2=32

8 0
2 years ago
Read 2 more answers
Suppose you invest 2500 at an annual interest rate of 7.5% compounded annually how much will you have in the account after 10 ye
Mnenie [13.5K]

Answer:

<u>The future value of this investment after 10 years is US$  5,152.58</u>

Step-by-step explanation:

1. Let's review the data given to us for solving the question:

Investment = US$ 2,500

Annual interest rate = 7.5% compounded annually

Duration of the investment = 10 years

2. Let's find the future value of this investment after 10 years, using the following formula:

FV = PV * (1 + r) ⁿ

Replacing with the real values, we have:

FV = 2,500 * (1 + 0.075) ¹⁰

FV = 2,500 * 1.0075¹⁰

FV = 2,500 * 2.06103

<u>FV = US$ 5,152.58</u>

5 0
3 years ago
Other questions:
  • Enter the phrase as an algebraic expression.<br><br> 53 less than j =?
    13·1 answer
  • Find the y-intercept for each of the new equations:
    6·1 answer
  • What percent of 130 is 96????<br> Round the the nearest whole percent
    13·2 answers
  • A professional football field is 160 feet wide. What is the width of the field in yards? *
    8·1 answer
  • Find the y-intercept for the equation y=15x-3
    10·1 answer
  • A shade of green paint is made by mixing blue paint and yellow paint in the ratio of 4 to 3. How many pints of blue paint and ye
    11·1 answer
  • What is 3-2y+(-8y)+8.4 as a simplified expression
    10·2 answers
  • What x-values are a solution to the system? Select each correct answer the answers are
    12·1 answer
  • Aaron runs a distance of 7.2km in the SE direction. How far east has Aaron run? Answer correct to one decimal point
    5·1 answer
  • Income Statements under Absorption Costing and Variable Costing
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!