SOLUTION: area of a rectangle= 220 square feet. find the diminensions of the figure.
----------- --------
x-9 | |
|
Algebra.Com
Question 178500: area of a rectangle= 220 square feet. find the diminensions of the figure.
--------------------
x-9 | |
| |
| |
--------------------
x
Found 2 solutions by nerdybill, jim_thompson5910:
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
Since we know that area of any rectangle is:
"width" * "length"
.
We then have:
x(x-9) = 220
x^2 - 9x = 220
x^2 - 9x - 220 =0
(x-20)(x+11) = 0
.
x = {20, -11}
.
We can toss out the negative solution leaving us with:
x = 20 feet
x-9 = 11 feet
.
Therefore, the dimensions are:
20 feet by 11 feet
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Let Length=x and Width=x-9 Note: the order does not matter, but the length is usually the longer of the two.
Start with the area of a rectangle formula
Plug in , and
Distribute
Subtract 220 from both sides.
Notice we have a quadratic equation in the form of where , , and
Let's use the quadratic formula to solve for x
Start with the quadratic formula
Plug in , , and
Negate to get .
Square to get .
Multiply to get
Rewrite as
Add to to get
Multiply and to get .
Take the square root of to get .
or Break up the expression.
or Combine like terms.
or Simplify.
So the possible answers are or
However, since you can't have a negative length, this means that only solution is
So the length is and the width is
==============================================
Answer:
So the length is 20 ft and the width is 11 ft
RELATED QUESTIONS
area of a rectangle= 220 square feet. find the dimensions of the figure
x-9 is the width (answered by solver91311)
A rectangle field is 40 feet wide and is enclosed by 220 feet of fencing. What is the... (answered by nerdybill)
The rectangle has a area of 60 square feet write and solve an equation to find the value... (answered by Alan3354)
a rectangle has an area of 84 square feet. the width is x and the length is x+5. find the (answered by josgarithmetic,math_helper)
A square has dimensions of x feet by x feet. A rectangle is 4 feet longer than the length (answered by scott8148)
a perimeter of a rectangle is 24 feet. if the width of the rectangle is X ft. how many... (answered by Fombitz)
What are the dimensions of a rectangle whose area is x^2-2x-143 square... (answered by mananth)
the length of a rectangle is three feet more than twice the width . the area of the... (answered by mananth)
A square has sides of length 3x cm. A rectangle is 2x cm by (x+7) cm. The area of the... (answered by josgarithmetic)