SOLUTION: We are in the section of solving equations by factoring. The question is: the length of the rectangle is 3 meters more than 2 times the width. If the area is 65 square meters, fin

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: We are in the section of solving equations by factoring. The question is: the length of the rectangle is 3 meters more than 2 times the width. If the area is 65 square meters, fin      Log On


   

Question 859080: We are in the section of solving equations by factoring.
The question is: the length of the rectangle is 3 meters more than 2 times the width. If the area is 65 square meters, find the width and length.
I keep getting fractions as answers, I know the equation for the Area of a rectangle is A=LW.
I keep plugging in 2x+3 but I am not getting the correct answer please help with the set up of the equation. Thank you.
Answer by Awesom3guy(31) About Me  (Show Source):
You can put this solution on YOUR website!

A+=+L%2AW
Now plug in 2W%2B3 instead of L
A+=+%282W%2B3%29%2AW
65+=+2W%5E2+%2B+3W

Now put the equation in standard form.
2W%5E2+%2B+3W+-+65+=+0

You want to factor. Separate the middle term into two parts:
2W%5E2+-+10W+%2B+13W+-+65+=+0
Factor the sides:
2W%28W+-+5%29+%2B+13%28W+-+5%29+=+0
Factor the bracket and what's not in it:
%282W+%2B+13%29%28W-5%29+=+0

Now what we have is two options:
2W+%2B+13+=+0, which gives that W equals -6.5, which is clearly not right.
W+-+5+=+0, which gives that W equals 5.

Now, from 65+=+L%2AW, compute for L.
L+=+65%2FW+=+65%2F5+=+13

Width of the triangle is 5 m and its length is 13 m. Also check.