SOLUTION: 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.

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.
.
If you add the sides of the given polygon you have:
.
8x + 3 + 6x + 4 + 6x - 3
.
If you combine the terms that contain x you get 8x + 6x + 6x = 20x
.
If you combine the constants you get 3 + 4 - 3 = +4
.
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:
.
20x + 4 = 84
.
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:
.
20x = 80
.
Then find x by dividing both sides of this equation by 20 ... the multiplier of the x. This
division leads to:
.
x = 80/20 = 4
.
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:
.
8x + 3 = 8(4) + 3 = 32 + 3 = 35
6x + 4 = 6(4) + 4 = 24 + 4 = 28
6x - 3 = 6(4) - 3 = 24 - 3 = 21
.
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.
.
Hope this helps you to understand the problem.
.
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