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The perimeter of a trapezoid is 33 meters. The length of the left and right sides are the same. See the figure below. If the length of the top is 6 meters more than a side and the length of the bottom is 11 meters more than the length of a side. Find the length of each side, the top and the bottom.

Please provide an explanation for how you did this!

User Alfakini
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1 Answer

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Answer: s = 4, s = 4, top side = 10, bottom side = 15

Explanation:

If you're working with a trapezoid that has a perimeter of 33 meters, you should know that the length of the top is 6 meters greater than the side (s+6), while the bottom is 11 meters greater than the length of the side (s+11). In order to solve for the side, you can use the equation s+6+s+11+s+s=33.

Slove s+6+s+11+s+s=33.

I solved an equation where the sum of several values equaled 33. By simplifying the equation, I found that one of the values (represented by "s") is equal to 4.

s+6+s+11+s+s=33

4s + 17 = 33

4s = 33-17

4s = 16

s=16/4

s=4

After determining that the value of the unknown side is 4, it is possible to substitute this value in four different equations...

s+6 = 4+6= 10

s+11 = 4+11 = 15

s = 4 (One of the sides)

s = 4 (The other side)

After solving the equations, it appears that both sides of the shape are equal to 4 units. The first equation, s+6=10, shows that when we subtract 6 from 10, we get 4. The second equation, s+11=15, shows that when we subtract 11 from 15, we also get 4. Therefore, the length of each side of the shape is 4 units.

User Ashish Thakkar
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