SOLUTION: Hello,
Not sure if I chose the right catorgory but I need help with the following problem.
The area of a rectangle is 55 square meters. Find the length and width of the rectan
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Question 195713: Hello,
Not sure if I chose the right catorgory but I need help with the following problem.
The area of a rectangle is 55 square meters. Find the length and width of the rectangle if its length is 6 meters greater than its width. Use an equation and the formula for area of a rectangle A = l × w
Thank you!
Found 2 solutions by ankor@dixie-net.com, jim_thompson5910:
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
The area of a rectangle is 55 square meters. Find the length and width of the rectangle if its length is 6 meters greater than its width. Use an equation and the formula for area of a rectangle A = l × w
:
It says,"if its length is 6 meters greater than its width.", therefore:
l = w + 6
:
Substitute (w+6) for l in the: l * w = 55
(w+6) * w = 55
w^2 + 6w = 55
w^2 + 6w - 55 = 0; a quadratic equation
Factor this to:
(w - 5)(w + 11) = 0
Positive solution is what we want here:
w = 5 m is the width
then
5 + 6 = 11 m is the length
;
:
Check solution: 11 * 5 = 55 sq/m
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
First, we'll use the area of a rectangle formula . Also, since "its length is 6 meters greater than its width", this means that
Start with the given equation.
Plug in
Rearrange the terms.
Distribute
Subtract 55 from both sides.
Notice we have a quadratic equation in the form of where , , and
Let's use the quadratic formula to solve for W
Start with the quadratic formula
Plug in , , and
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, a negative width doesn't make much sense. So this means we'll ignore
So the solution is which makes the width 5 meters.
Go back to the second equation
Plug in
Add
So the length is 11 meters.
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