SOLUTION: find the permiter of the given figure the figure is a rectangle the top is x over -2x-5 and right side is x over 2x-5

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Question 83936: find the permiter of the given figure
the figure is a rectangle
the top is
x
over
-2x-5
and right side is
x
over
2x-5
Answer by tutor_paul(519) About Me  (Show Source):
You can put this solution on YOUR website!
You know that the perimeter of a rectangle is the sum of all 4 sides. Since you are given the length and the width, the perimeter of the rectangle is given by:
P=%282%2AL%29%2B%282%2AW%29
In this case,
P=%282x%2F%282x-5%29%29%2B%282x%2F%28-2x-5%29%29
Before we get into adding these up, I want to rewrite the 2nd term, since all those minus signs are giving me a headache :-)
P=%282x%2F%282x-5%29%29-%282x%2F%282x%2B5%29%29
So now you need to add these up. Recall back in the day when you had to add fractions with different denominators. You had to find the LCD. The same concept applies here. Like those good old days, you could always multiply the 2 denominators together to get an LCD (or at least a CD) as a last resort. You can apply the same principle here. Your LCD is:
%282x-5%29%282x%2B5%29
So I can rewrite the problem like this:
P=%282x%282x%2B5%29-2x%282x-5%29%29%2F%28%282x-5%29%282x%2B5%29%29
Now, simplify the numerator by multiplying it out first:
P=%284x%5E2%2B10x-4x%5E2%2B10x%29%2F%28%282x-5%29%282x%2B5%29%29
The 4x^2 terms go away, and this leaves you with:
P=%2820x%29%2F%28%282x-5%29%282x%2B5%29%29
I will go ahead and multiply out that denominator, but you really don't have to:
highlight%28P=20x%2F%284x%5E2-25%29%29
Good Luck,
tutor_paul@yahoo.com