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2 years ago

13

The perimeter of a trapezoid is 39a – 7. Three sides have the following lengths: 9a, 5a + 1, and 17a – 6. What is the length of

the fourth side?
A. 12
B.a – 7
C. 8a – 2
D.31a – 5

2 answers:

Pie2 years ago

6 0

Answer: 8a-2

Step-by-step explanation:

The perimeter of a trapezoid is the addition of its four sides.

Perimeter of trapezoid= 39a – 7.

Length of 1st side= 9a,

Length of 2nd side= 5a + 1,

Length of third side= 17a – 6.

Length of the fourth side= Unknown

To find the length of the 4th side, we add the length of the three sides together and subtract from the perimeter of the trapezoid. This will be:

= 39a-7 - (9a+5a+1+17a-6)

= 39a-7-(9a+5a+17a+1-6)

= 39a-7-(31a-5)

=39a-7-31a+5

= 39a-31a-7+5

= 8a-2

The length of the 4th side is 8a-2

Airida [17]2 years ago

3 0

We know the perimeter is the total sum of all sides of the shape, we can use this to form an equation: the perimeter=1st side + 2nd side + 3rd side + 4th side 39a-7=9a+(5a+1)+(17a-6)+4th side.
Collect like terms to get 39a-7=31a-5+4th side
If we move everything but the 4th side over to the left we can solve
C. 8a-2=4th side is the correct answer

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ollegr [7]

Answer:

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Step-by-step explanation:

From the figure we can infer that our triangle has vertices A = (-5, 4), B = (1, 4), and C = (3, -4).

First thing we are doing is find the lengths of AB, BC, and AC using the distance formula:

$d=\sqrt{(x_2-x_1)^{2} +(y_2-y_1)^{2}}$

where

$(x_1,y_1)$ are the coordinates of the first point

$(x_2,y_2)$ are the coordinates of the second point

- For AB:

$d=\sqrt{[1-(-5)]^{2}+(4-4)^2}$

$d=\sqrt{(1+5)^{2}+(0)^2}$

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- For BC:

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$d=\sqrt{(2)^{2} +(-8)^{2}}$

$d=\sqrt{4+64}$

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- For AC:

$d=\sqrt{[3-(-5)]^{2} +(-4-4)^{2}}$

$d=\sqrt{(3+5)^{2} +(-8)^{2}}$

$d=\sqrt{(8)^{2} +64}$

$d=\sqrt{64+64}$

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Next, now that we have our lengths, we can add them to find the perimeter of our triangle:

$p=AB+BC+AC$

$p=6+8.24+11.31$

$p=25.55$

$p=25.6$

We can conclude that the perimeter of the triangle shown in the figure is 25.6 units.

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Lubov Fominskaja [6]

I strongly believe the answer is c
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