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IgorLugansk [536]
3 years ago
12

On a coordinate plane, square A B C D is shown. Point A is at (3, 4), point B is at (2, negative 2), point C is at (negative 4,

negative 1), and point D is at (negative 3, 5). What is the perimeter of square ABCD? StartRoot 37 EndRoot units 4 StartRoot 37 EndRoot units 28 units 37 units

Mathematics
1 answer:
kondaur [170]3 years ago
6 0

Answer:

4\sqrt{37}

Step-by-step explanation:

Since the figure is a square, find the length of 1 side and multiply by 4 for perimeter.

Calculate the length of AB using the distance formula.

AB = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = A(3, 4) and (x₂, y₂ ) = B(2, - 2)

AB = \sqrt{(2-3)^2+(-2-4)^2}

     = \sqrt{(-1)^2+(-6)^2}

     = \sqrt{1+36}

     = \sqrt{37}

Hence

perimeter = 4AB = 4\sqrt{37}

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2 years ago
A circle is cut into congruent sections and arranged to form a figure that approximates a parallelogram. Find the approximate he
Solnce55 [7]

Answer:

<h2>The height is 3.43 centimeters, approximately.</h2>

Step-by-step explanation:

Notice that there are 16 pieces from the circle, which means each sector has an angle of

\theta = \frac{360\°}{16}=22.5\°

Where all sectors have equal area.

Now, the area of the whole circle is 12.25 \pi \ cm^{2}, if we use the formula of its area, we'll find the radius of the circle

A= \pi r^{2}\\ 12.25\pi = \pi r^{2}\\ r=\sqrt{12.25} \approx  3.5

Notice that each piece works as an isosceles triangle, because each side is the radius, that is, they have the same length. So far, we know the sides of the isosceles triangle and one internal angle.

To find the height of the one piece, we need to use trigonometric reasons, because the height divides a triangle in two equal right triangles.

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6 0
3 years ago
Which relationship is always true for the angles r, x, y, and z of triangle ABC?
mariarad [96]

That's the second one,


180 - x = r


Whenever two lines cross we get congruent opposite angles and supplemental adjacent angles, i.e. they add to 180 degrees.


The first one is almost right; we have r+y+z=180 and r+x=180 so x=y+z not quite what was written.


3 0
3 years ago
Could someone answer these 3 for me?
KengaRu [80]

Answer:

x=4.77

Angle 3=98.32 degrees

Angle 6= 81.68 degrees

Step-by-step explanation:

(Assuming these are parallel lines), Angle 3 and angle 5 are equal because they are alternate Angles. Therefore we can write the following equation to solves for x:

16x+22=3x+84 (angle 3=angle5)

Which we can now solve:

16x +22 - 22 - 3x=3x-3x+84-22

13x=62

13x/13=62/13

x=4.77 (2dp)

We can then use this x to calculate angle 3:

16(4.77)+22

76.33+22=98.32 degrees

Finally,

Angle 6 and angle 3 are interior angles, so they add up to 180 degrees.

So to find angle 6,we can just subtract angle 3 from 180:

180-98.32=81.68 degrees.

Hope this helped!

6 0
3 years ago
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