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Fynjy0 [20]
3 years ago
12

Find the perimeter of Triangle ABC with the verticies A(-5,5) B(3,-5) and C(-5,1

Mathematics
1 answer:
finlep [7]3 years ago
8 0

Hello!
 
Let's calculate a distance between two points using the Pythagorean theorem:<span>

</span>d ^ 2_ {AB} = (x_ {B} - x_ {A}) ^ 2 + (y_ {B} - y_ {A}) ^ 2

Data:

x_B = 3 &#10;&#10;x_A = -5 &#10;&#10;y_B = -5 &#10;&#10;y_A = 5 &#10;&#10;d_ {AB} =?

Solving: distance from A to B

d^ 2_ {AB} = (x_ {B} - x_ {A}) ^ 2 + (y_ {B} - y_ {A}) ^ 2 &#10;&#10;d^ 2_ {AB} = (3 - (-5)) ^ 2 + (-5 - 5) ^ 2 &#10;&#10;d^ 2_ {AB} = (8) ^ 2 + (-10) ^ 2 &#10;&#10;d^ 2_ {AB} = 64 + 100 &#10;&#10;d^ 2_ {AB} = 164 &#10;&#10;d_{AB} = \sqrt {164} &#10;&#10;d_{AB} = \sqrt {2 ^ 2 * 41} &#10;&#10;\boxed {d_ {AB} = 2 \sqrt {41}}

<span>Solving:
 
distance from A to C</span>

d ^ 2_ {AC} = (x_ {C} - x_ {A}) ^ 2 + (y_ {C} - y_ {A}) ^ 2

Data:

x_C = -5&#10; &#10;x_A = -5&#10; &#10;y_C = 1 &#10;&#10;y_A = 5 &#10;&#10;d_ {AC} =?


d^ 2_ {AC} = (x_ {C} - x_ {A}) ^ 2 + (y_ {C} - y_ {A}) ^ 2 &#10;&#10;d^ 2_ {AC} = (-5 - (-5)) ^ 2 + (1 - 5) ^ 2 &#10;&#10;d^ 2_ {AC} = (0) ^ 2 + (-4) ^ 2  &#10;&#10;d^ 2_ {AC} = 0 + 16  &#10;&#10;d^ 2_ {AC} = 16 &#10;&#10;d_ {AC} = \sqrt {16} &#10;&#10;\boxed {d_ {AC} = 4}&#10;<span>
</span>

Solving:

distance from B to C

d^ 2_ {BC} = (x_ {C} - x_ {B}) ^ 2 + (y_ {C} - y_ {B}) ^ 2

Data:

x_C = -5 &#10;&#10;x_B = 3 &#10;&#10;y_C = 1 &#10;&#10;y_B = -5 &#10;&#10;d_ {BC} =?


d^ 2_ {BC} = (x_ {C} - x_ {B}) ^ 2 + (y_ {C} - y_ {B}) ^ 2&#10; &#10;d^ 2_ {BC} = (-5 - 3) ^ 2 + (1 - (-5)) ^ 2&#10;&#10;d^ 2_ {BC} = (-8) ^ 2 + (6) ^ 2  &#10;&#10;d^ 2_ {BC} = 64 + 36&#10;&#10;d^ 2_ {BC} = 100 &#10;&#10;d_ {BC} = \sqrt {100}&#10;&#10;\boxed {d_ {BC} = 10}

<span>Now let's calculate the perimeter of the triangle ABC, knowing that the perimeter is the sum of the sides, then:
</span>
p = d_ {AB} + d_ {AC} + d_ {BC}  &#10;&#10;

p = 2\sqrt {41} + 4 + 10

&#10;\boxed {\boxed {p = 14 + 2 \sqrt {41}}} \end {array}} \qquad \quad \checkmark
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7. The diagram shows a regular pentagon inscribed inside the rectangle. Find the values of x, y, and z.
Wewaii [24]
<span>regular pentagon sum of interior = (5 - 2) x 180 = 3 x 180 = 540
so
x = 540 / 5 = 108

180 - 108 = 72
y = 72/2 = 36

z = 180 - 90 - 36
z = 54

answer
x = 108, y = 36 and z = 54</span>
3 0
3 years ago
Who can help me with this :)
babymother [125]

Answer:

90 im not sure tho but hopefully its correct

7 0
2 years ago
Can you help <br> please and thank you
seraphim [82]

Answer:

C

Step-by-step explanation:

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7 0
2 years ago
Read 2 more answers
Select the procedure that can be used to show the converse of the Pythagorean theorem using side lengths chosen from 3 feet, 4 f
aksik [14]

Using Pythagoras theorem,  we know that 3² + 4² = 5², draw the 3-foot side and the 4-foot side with a right angle between them. The 5-foot side will fit to form a right triangle

<h3>How to use Pythagoras theorem to prove a right triangle?</h3>

The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.

Therefore,

c²= a²+ b²

where

  • c = hypotenuse side
  • a and b are the other legs.

Therefore,

3² + 4² = 5²

Hence,

Knowing that 3² + 4² = 5², draw the 3-foot side and the 4-foot side with a right angle between them. The 5-foot side will fit to form a right triangle

learn more on Pythagoras's theorem here: brainly.com/question/20462170

#SPJ1

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2 years ago
WILL GIVE BRANLIEST.
Tju [1.3M]

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1. True

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7. Jesus.

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3 years ago
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