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Question 119875This question is from textbook GEOMETRY
: THIS IS THE QUESTION FROM MY BOOK: FIND THE LENGTH OF EACH SIDE OF THE POLYGON FOR THE GIVEN PERIMETER. P=84 AND THE SIDES ARE 8X+3, 6X+4, 6X-3. PLEASE HELP ME.
This question is from textbook GEOMETRY
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! The perimeter of a polygon is the sum of the lengths of all its sides.
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If you add the sides of the given polygon you have:
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8x + 3 + 6x + 4 + 6x - 3
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If you combine the terms that contain x you get 8x + 6x + 6x = 20x
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If you combine the constants you get 3 + 4 - 3 = +4
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So the sum of all the sides reduces to 20x + 4 and since it is the perimeter, you can set it
equal to 84 as follows:
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20x + 4 = 84
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Solve by first getting rid of the 4 on the left side. Do that by subtracting 4 from both
sides of the equation to get:
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20x = 80
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Then find x by dividing both sides of this equation by 20 ... the multiplier of the x. This
division leads to:
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x = 80/20 = 4
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Now that you know x is equal to 4 you can find the lengths of the three sides by substituting
4 for x in each of the three sides to get:
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8x + 3 = 8(4) + 3 = 32 + 3 = 35
6x + 4 = 6(4) + 4 = 24 + 4 = 28
6x - 3 = 6(4) - 3 = 24 - 3 = 21
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So the lengths of the three sides are 35, 28, and 21. If you add these three sides you
find that the perimeter is 35 + 28 + 21 = 84 ... just as the problem said it should be.
This check verifies that the answers are correct.
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Hope this helps you to understand the problem.
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