SOLUTION: The width of a rectangle is the length minus 6 units. The area of the rectangle is 27 units. What is the length and width of the rectangle?

Algebra.Com
Question 1198616: The width of a rectangle is the length minus 6 units. The area of the rectangle is 27 units. What is the length and width of the rectangle?
Found 2 solutions by Theo, MathTherapy:
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
A = area
L = length
W = width

A = L * W
W = L - 6
A = L * (L - 6)

A = 27
27 = L * (L - 6)
L * (L - 6) = L^2 - 6L
27 = L^2 - 6L
subtract 27 from both sides of that equation to get:
L^2 - 6L - 27 = 0
factor that quadratic equation to get:
(L - 9) * (L + 3) = 0
L = 9 or L = -3.
L can't be -3, so L = 9
W = L - 6 makes W = 3

dimensions are:
L = 9
W = 3
A = L * W = 9 * 3 = 27

length of the rectangle is 9 units and width of the rectangle is 3 units.
that's your solution.

requirements of the problem are solved, since length of 9 units minus 6 units is equal to 3 units which is the width.



Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
The width of a rectangle is the length minus 6 units. The area of the rectangle is 27 units. What is the length and width of the rectangle?
All you need for this is 2 numbers that have a product of 27, and a difference of 6. Obviously those 2 numbers are 9 amnd 3.
Since the length is the longer of the 2, and the width is the shorter, LENGTH = 9, and WIDTH = 3.

You DON'T NEED equations to solve this. As a matter oof fact, if you do use equations, you come right back to asking yourself
the same question in order to solve the equation: "What 2 numbers have a product of 27, and a difference of 6."
RELATED QUESTIONS

The length of a rectangle is the width minus 2 units. The area of the rectangle is 8... (answered by Cromlix)
a rectangle has width 15 units AND AREA 300 SQUARE UNITS WHAT IS THE LENGTH OF THE... (answered by jim_thompson5910)
What is the area of a rectangle whose width is 6 units more than its... (answered by josgarithmetic)
the length of a rectangle is 3x+2 units and the width is x-6 units, what is the perimeter (answered by stanbon)
A rectangle has a length of n units. Its width is 6 units less than its length. What is... (answered by josgarithmetic)
A rectangle has an area of 24 square units. The width is 5 units less than the length. (answered by RAY100)
a rectangle has an area of 24 square units .the width is 5 units less than the length .... (answered by Alan3354)
The length of a rectangle exceeds its width by 7 units and its area is 228 square units.... (answered by Alan3354)
The length of a rectangle exceeds its width by 7 units and its area is 228 square units.... (answered by scott8148,2332)