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

Algebra ->  Polynomials-and-rational-expressions -> 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      Log On


   

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) About Me  (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) About Me  (Show Source):
You can put this solution on YOUR website!
First, we'll use the area of a rectangle formula A=LW. Also, since "its length is 6 meters greater than its width", this means that L=W%2B6


A=LW Start with the given equation.


55=%28W%2B6%29W Plug in L=W%2B6


55=W%28W%2B6%29 Rearrange the terms.


55=W%5E2%2B6W Distribute


0=W%5E2%2B6W-55 Subtract 55 from both sides.


Notice we have a quadratic equation in the form of 0=aW%5E2%2BbW%2Bc where a=1, b=6, and c=-55


Let's use the quadratic formula to solve for W


W+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 Start with the quadratic formula


W+=+%28-%286%29+%2B-+sqrt%28+%286%29%5E2-4%281%29%28-55%29+%29%29%2F%282%281%29%29 Plug in a=1, b=6, and c=-55


W+=+%28-6+%2B-+sqrt%28+36-4%281%29%28-55%29+%29%29%2F%282%281%29%29 Square 6 to get 36.


W+=+%28-6+%2B-+sqrt%28+36--220+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-55%29 to get -220


W+=+%28-6+%2B-+sqrt%28+36%2B220+%29%29%2F%282%281%29%29 Rewrite sqrt%2836--220%29 as sqrt%2836%2B220%29


W+=+%28-6+%2B-+sqrt%28+256+%29%29%2F%282%281%29%29 Add 36 to 220 to get 256


W+=+%28-6+%2B-+sqrt%28+256+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


W+=+%28-6+%2B-+16%29%2F%282%29 Take the square root of 256 to get 16.


W+=+%28-6+%2B+16%29%2F%282%29 or W+=+%28-6+-+16%29%2F%282%29 Break up the expression.


W+=+%2810%29%2F%282%29 or W+=++%28-22%29%2F%282%29 Combine like terms.


W+=+5 or W+=+-11 Simplify.


So the possible answers are W+=+5 or W+=+-11


However, a negative width doesn't make much sense. So this means we'll ignore W+=+-11


So the solution is W+=+5 which makes the width 5 meters.


L=W%2B6 Go back to the second equation


L=5%2B6 Plug in z+=+5


L=11 Add


So the length is 11 meters.