SOLUTION: I need to answer this question using quadratics and I am not sure where to start. Ed needs to enclose a rectangular section of his yard. The area is 35 sq ft and the perimeter is 2

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: I need to answer this question using quadratics and I am not sure where to start. Ed needs to enclose a rectangular section of his yard. The area is 35 sq ft and the perimeter is 2      Log On


   

Question 166189: I need to answer this question using quadratics and I am not sure where to start. Ed needs to enclose a rectangular section of his yard. The area is 35 sq ft and the perimeter is 27 ft. Find the length and the width of the section.
Found 2 solutions by vleith, Mathtut:
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
Perimeter is the length 'around' the rectangular area. P+=+2L+%2B+2W
Area is the area of the enclosed rectangle A+=+L+%2A+W
27+=+2L+%2B+2W
27-2W+=+2L+
%2827-2W%29%2F2+=+L+
A+=+L+%2A+W
35+=+%28%2827-2W%29%2F2%29++%2A+W+
35+=+%2827W+-+2W%5E2%29%2F2+
70+=+27W+-+2W%5E2
2W%5E2+-+27W+%2B+70+=+0
Now use the quadratic equation to solve
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B-27x%2B70+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-27%29%5E2-4%2A2%2A70=169.

Discriminant d=169 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--27%2B-sqrt%28+169+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-27%29%2Bsqrt%28+169+%29%29%2F2%5C2+=+10
x%5B2%5D+=+%28-%28-27%29-sqrt%28+169+%29%29%2F2%5C2+=+3.5

Quadratic expression 2x%5E2%2B-27x%2B70 can be factored:
2x%5E2%2B-27x%2B70+=+2%28x-10%29%2A%28x-3.5%29
Again, the answer is: 10, 3.5. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-27%2Ax%2B70+%29

Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
since A=lw where l is length and w is the width
and P=2(l+w)
we plug in the known values
35=lw
27=2(l+w)--->27/2=l+w---->l=27/2-w---->l=(27-2w)/2
place value of l into 1st equation----->35=((27-2w)/2)(w)----->70=27w-2w%5E2
2w%5E2-27w%2B70=0 factoring (2w-7)(w-10) so w=7/2,10
when w=7/2 l=10 when w=10 l=7/2 width=+%287%2F2%29+length=+%2810%29