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blsea [12.9K]
4 years ago
15

A right triangular prism is constructed so that its height is equal to the leg length of the base.

Mathematics
1 answer:
Effectus [21]4 years ago
6 0

Answer:

V = \frac{1}{2} x^{3}  cubic units

Step-by-step explanation:

Given the information

  • A right triangular prism has the height is equal to the leg length of the base.
  • The right triangles have 2 sides with a length of x

=> the height  = x  

As we know, the formula used to determine the volume of a right triangular prism is:

V = The base area * the height

In this situation, we have

V = (\frac{1}{2} *x*x)*x

<=> V = \frac{1}{2} x^{3} cubic units  

Hope it will find you well

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What is the height of the triangle? 12 units 24 units 36 units 72 units.
konstantin123 [22]

Height of the triangle is the altitude of the triangle and which is drawn perpendicular from the vertex of the triangle to the opposite side. The height of the tringle is 24 units. Hence option 2 is the correct option.

<h3>Given information-</h3>

The triangle for the given problem is shown in the image below.

Form the figure the length of the each side is 16 \sqrt{3} units.

As all the sides are equal thus the \Delta MNO is a equilateral triangle in which the height of the divides the triangle into two equal part of the length 8\sqrt{3} at point <em>R.</em>

<h3>Height of the triangle-</h3>

Height of the triangle is the altitude of the triangle and which is drawn perpendicular from the vertex of the triangle to the opposite side.

Now in the  \Delta MRN, the length of the hypotenuse is 16 \sqrt{3} units and the length of the base is 8\sqrt{3} units. Let <em>h </em>is the height of the triangle thus by the Pythagoras theorem,

(16\sqrt{3})^2 =(8\sqrt{3})^2+h^2

Solve for <em>h,</em>

<em />

<em />\begin{aligned}h^2 &=(16\sqrt{3})^2 -(8\sqrt{3})^2\\h^2 &=16\times16\times3 -8\times8\times3\\h^2 &=576\\h &=\sqrt{576}\\h &=24\\\end<em />

<em />

Thus the height of the tringle is 24 units. Hence option 2 is the correct option.

Learn more about the equilateral triangle here;

brainly.com/question/4268382

5 0
2 years ago
measure a and measure b are vertical angles with measure a = x and measure b = 4x - 30. what is measure a?
Zolol [24]

Answer:

∠a = 10°

Step-by-step explanation:

The measure of ∠a = x

The measure of ∠b = 4x-30

It is also mentioned that the measure a and measure b are vertical angles. We need to find the value of a.

For vertically opposite angles,

∠a = ∠b

x = 4x-30

or

4x-30=x

Taking like terms together,

4x-x= 30

3x = 30

x = 10

So, the meausre of ∠a is equal to 10°.

3 0
3 years ago
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4 years ago
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Write an equation of the line that passes through (2,-1) and is parallel to the graph of y = 5x – 2. Write your final equation i
slamgirl [31]

Answer:

The equation would be y = 5x - 11

Step-by-step explanation:

To find this line, start with the slope. Since it is parallel to the first line and parallel lines have the same slope, we know the slope to be 5. Given this we can use point-slope form and solve for y to get the equation.

y - y1 = m(x - x1)

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Alexus [3.1K]

Answer:

0.125

Step-by-step explanation:

5/40 simulated results were at or below mean 16.5

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