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Crazy boy [7]
2 years ago
10

Find the value of x PLEASE EXPLAIN

Mathematics
2 answers:
dedylja [7]2 years ago
7 0

We can say that:

  • In the first triangle, x = 57°
  • In the second triangle, x = 111°

<h2>Let's go!</h2>

We must know that the sum of all the internal angles of a triangle is equal to 180°. So, just solve an equation to determine x in each triangle.

<h3>First triangle:</h3>
  • 67 + 56 + x = 180 → Sum:
  • 123 + x = 180 → We move 123 to the other side, changing its signal.
  • x = 180 - 123 → Subtract:
  • <u>x = 57°</u>
<h3>Second triangle:</h3>
  • 22 + 47 + x = 180 → Sum:
  • 69 + x = 180 → We move 69 to the other side, changing its signal.
  • x = 180 - 69 → Subtract:
  • <u>x = 111°</u>

<u>________________</u>

<em>Hope this helps! Good studies! </em>☺

Wewaii [24]2 years ago
6 0

Answer:

x = 57, x = 111

Step-by-step explanation:

The sum of the 3 angles in a triangle = 180°

Sum the 3 angles and equate to 180, that is

x + 67 + 56 = 180

x + 123 = 180 ( subtract 123 from both sides )

x = 57

---------------------------------------------------------------------

Similarly

x + 47 + 22 = 180

x + 69 = 180 ( subtract 69 from both sides )

x = 111

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Let
x-----> the length of rectangle
y-----> the width of rectangle

we know that 
perimeter of rectangle=2*[x+y]
perimeter of rectangle=82 m
82=2*[x+y]---> divide by 2 both sides---> 41=x+y--> y=41-x---> equation 1

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substitute equation 1 in the area formula
Area=x*[41-x]----> 41x-x²

using a graph tool
see the attached figure

the vertex is the point (20.5,420.25)
that means
 for x=20.5 m ( length of rectangle)
the area is 420.25 m²

y=420.25/20.5----> 20.5 m

the dimensions are
20.5 m x 20.5 m------> is a square

the answer part 1) 
<span>the dimensions of the rectangular with Maximum area is a square with length side 20.5 meters
</span>
Part 2)<span>b) Suppose 41 barriers each 2m long, are used instead. Can the same area be enclosed?
</span>divide the length side of the square by 2
so
20.5/2=10.25--------> 10 barriers
the dimensions are 10 barriers x 10 barriers
10 barriers=10*2---> 20 m

the area enclosed with barriers is =20*20----> 400 m²

400 m² < 420.25 m²
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the answer Part 2) is 
<span>the area enclosed by the barriers is less than the area enclosed by the rope
</span>
Part 3)<span>How much more area can be enclosed if the rope is used instead of the barriers
</span>
area using the rope=420.25 m²
area using the barriers=400 m²

420.25-400=20.25 m²

the answer part 3) is
20.25 m²

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