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pentagon [3]
2 years ago
14

The triangle and the trapezoid have the same area. Base b2 is twice the length of base b1. What are the lenghts of the bases of

the trapezoid. The triangle is 2lcm base and 6cm height. decompose the triangle
Mathematics
2 answers:
Sati [7]2 years ago
8 0

Answer:

<h2>The lengths of the bases of the trapezoid:</h2><h2>42/h cm and 84/h cm.</h2>

Step-by-step explanation:

The formula of an area of a triangle:

A=\dfrac{bh}{2}

<em>b</em><em> </em>- base

<em>h</em> - height

We have <em>b = 21cm, h = 6cm</em>.

Substitute:

A=\dfrac{(21)(6)}{2}=63\ cm^2

The formula of an area of a trapezoid:

A=\dfrac{b_1+b_2}{2}\cdot h

<em>b₁, b₂</em> - bases

<em>h</em><em> - </em>height

We have <em>b₁ = 2b₂</em>, therefore <em>b₁ + b₂ = 2b₂ + b₂ = 3b₂</em>.

The area of a triangle and the area of a trapezoid are the same.

Therefore

\dfrac{3b_2}{2}\cdot h=63         <em>multiply both sides by 2</em>

3b_2h=126          <em>divide both sides by 3</em>

b_2h=42         <em>divide both sides by h</em>

b_2=\dfrac{42}{h}

b_1=2b_2\to b_1=2\cdot\dfrac{42}{h}=\dfrac{84}{h}

Scrat [10]2 years ago
6 0

Answer:

The length of the bases of the trapezoid is b_1=42H and b_2=84H      

Step-by-step explanation:

Given : The triangle and the trapezoid have the same area. Base b_2 is twice the length of base b_1.

To find : What are the lengths of the bases of the trapezoid. The triangle is 21 cm base and 6 cm height decompose the triangle?

Solution :

The area of the triangle is A_t=\frac{1}{2}bh

The triangle is 21 cm base and 6 cm height,

A_t=\frac{1}{2}\times 21\times 6

A_t=63\ cm^2

The area of the trapezoid is A_T=\frac{b_1+b_2}{2}H

The triangle and the trapezoid have the same area.

i.e. 63=\frac{b_1+b_2}{2}H

Base b_2 is twice the length of base b_1

i.e. b_2=2b_1

Substitute,

63=\frac{b_1+2b_1}{2}H

63=\frac{3b_1}{2}H

126=(3b_1)H

\frac{126}{3H}=b_1

b_1=42H

Put in b_2=2b_1,

b_2=2(42H)

b_2=84H

The length of the bases of the trapezoid is b_1=42H and b_2=84H

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At Friday's football game, 1,294 tickets were sold for a total amount of $8,816.00. If each student ticket costs $5.00, and each
NeTakaya

Answer:

512 student tickets.

Step-by-step explanation:

Let x be number of student tickets and y be number of adult tickets.

We have been given that at Friday's football game 1,294 tickets were sold. We can represent this information as:

x+y=1294...(1)

We are also told that each student ticket costs $5.00, and each adult ticket costs $8.00 and 1,294 tickets were sold for a total amount of $8,816. We can represent this information as:

5x+8y=8,816...(2)

From equation (1) we will get,

y=1294-x

Substituting this value in equation (2) we will get,

5x+8(1294-x)=8,816

5x+10352-8x=8,816

-3x+10352=8,816

-3x=8,816-10352

-3x=-1536

x=\frac{-1536}{-3}

x=512

Therefore, 512 student tickets were purchased at Fridays football game.

6 0
3 years ago
Given the equation 2(3x − 4) = 5x + 6, solve for the variable. Explain each step and justify your process.
blagie [28]
2(3x-4) = 5x+6
First, expand the bracket.
6x-8=5x+6
Next, move the variables to the same side.
x-8=6
Move the -8 to the other side, change to +
x=6+8
x=14
Charlie’s solution is incorrect. When expanding the bracket, he changed the - to a +.
6 0
2 years ago
What are the special right triangle measures?
erik [133]
The hypotenuse is 2x, the base is x*sqrt(3) and the left base if x
5 0
3 years ago
WILL MARK BRAINLIEST PLEASE SHOW WORK :)
Solnce55 [7]

Answer:

<em>(1). A = 18 cm² ; (2). TR = 18 units</em>

Step-by-step explanation:

6 0
3 years ago
In Image:
iris [78.8K]

Answer:

The answer to your question is          x ≠ -10   x ≠ 2     x ≠ -2

Solution                                                \frac{(x- 8)(x + 2)}{(x + 8)(x - 2)}      

Step-by-step explanation:

Process

1.- Factor all the polynomials

              \frac{x^{2} -3x - 40}{x^{2} + 8x - 20} / \frac{x^{2}+ 13x + 40}{x^{2}+ 12x + 20} = \frac{(x-8)(x + 5)}{(x + 10)(x- 2)} / \frac{(x+ 8)(x + 5)}{(x + 10)(x + 2)}

2.- Invert the second term

                                             = \frac{(x- 8)(x + 5)}{(x +10)(x - 2)}  \frac{(x+ 10)(x + 2)}{(x + 8)(x +5)}

3.- Simplify

                                              = \frac{(x- 8)(x + 2)}{(x + 8)(x - 2)}

4.- x must be different to

            x ≠ -10   x ≠ 2     x ≠ -2

This values are from the factor expressions and then equal to zero.

8 0
3 years ago
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