SOLUTION: a REctangle with an area of 84 square centimeteres is 5 centimeters longer than it is wide. Find its perimeter? How am i supposed to work this out? I'm stuck on this problem and m

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Question 470801: a REctangle with an area of 84 square centimeteres is 5 centimeters longer than it is wide. Find its perimeter? How am i supposed to work this out? I'm stuck on this problem and my notes don't help , and the net formulas don't help either.
Answer by ccs2011(207) (Show Source):
You can put this solution on YOUR website!
Before you can solve for the perimeter, you must find the dimensions of the rectangle.
Let x be the width, thus the length is (x+5).
The area of a rectangle is Length*Width.
This gives us the equation:

Distribute left side

This is a quadratic equation, to solve first set equal to zero.
Subtract 84 on both sides

Solve for x by factoring or using quadratic formula.
This factors nicely.
Look for factors of -84 that add up to 5.
84 + -1 = 83
42 + -2 = 40
21 + -4 = 17
7 + -12 = -5 OR -7 + 12 = 5
Thus equation can be rewritten as follows:

x-7 = 0 --> x = 7
x+12 = 0 --> x = -12
x must be positive, therefore x = 7.
If the width is 7 then the length must be 12.
Now substitute these values in to find perimeter:

Therefore the perimeter of the rectangle is 38 cm.