SOLUTION: The length of the top of a table is 4m greater than the width. The area is 77m^2. Find the dimensions of the table

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: The length of the top of a table is 4m greater than the width. The area is 77m^2. Find the dimensions of the table      Log On


   

Question 446322: The length of the top of a table is 4m greater than the width. The area is 77m^2. Find the dimensions of the table
Answer by chriswen(106) About Me  (Show Source):
You can put this solution on YOUR website!
Let x m be the width of the table.
Let x+4 m be the length of the table.
...
l%2Aw=A
%28x%2B4%29%28x%29=77
x%5E2%2B4x=77
x%5E2%2B4x-77=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B4x%2B-77+=+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=%284%29%5E2-4%2A1%2A-77=324.

Discriminant d=324 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-4%2B-sqrt%28+324+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%284%29%2Bsqrt%28+324+%29%29%2F2%5C1+=+7
x%5B2%5D+=+%28-%284%29-sqrt%28+324+%29%29%2F2%5C1+=+-11

Quadratic expression 1x%5E2%2B4x%2B-77 can be factored:
1x%5E2%2B4x%2B-77+=+1%28x-7%29%2A%28x--11%29
Again, the answer is: 7, -11. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B4%2Ax%2B-77+%29

Since the answer must be positive,
x=7
x+4=11
Therefore the dimensions of the table are 7m by 11m.