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

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.

RELATED QUESTIONS
a rectangle with a perimeter of 40 centimeters is 5 centimeters longer than twice its... (answered by checkley77)

A rectangle is 5 feet longer than it is wide, and its area is 66 square feet. Find its... (answered by scott8148)

A rectangle is 5 feet longer than it is wide, and its area is 66 square feet. Find its... (answered by edjones)

Please help me solve the following equation, "A rectangle is 2 centimeters longer than it (answered by lwsshak3,josmiceli)

a book is 5 cm longer than it is wide. if it has an area of 84 sq cm, find its... (answered by sachi)

Dimensions of a Rectangle A rectangle is 5 feet longer than it is wide and has an area... (answered by oberobic)

A rectangle is 4 times as long as it is wide. A second rectangle is 5 centimeters longer... (answered by JBarnum,MathTherapy)

A parallelogram has an area of 84 square centimeters and a base that is 5 centimeters... (answered by kittycat1613)

The area of a rectangle is 48 square centimeters. If the length of the rectangle is 8... (answered by RAY100)