SOLUTION: the perimeter is 47, one length is x+4 another one is x+5 the other 3x-2 and the last x^2-2x

Algebra ->  Polygons -> SOLUTION: the perimeter is 47, one length is x+4 another one is x+5 the other 3x-2 and the last x^2-2x      Log On


   

Question 433415: the perimeter is 47, one length is x+4 another one is x+5 the other 3x-2 and the last x^2-2x
Answer by jorel1380(3719) About Me  (Show Source):
You can put this solution on YOUR website!
x2-2x+3x-2+x+5+x+4=47
x2+3x+7=47
x2+3x-40=0
(x+8)(x-5)=0
x=-8,5
Throwing out the negative answer, we get x=5.
The sides are 9,10,13,15.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B3x%2B-40+=+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=%283%29%5E2-4%2A1%2A-40=169.

Discriminant d=169 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-3%2B-sqrt%28+169+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%283%29%2Bsqrt%28+169+%29%29%2F2%5C1+=+5
x%5B2%5D+=+%28-%283%29-sqrt%28+169+%29%29%2F2%5C1+=+-8

Quadratic expression 1x%5E2%2B3x%2B-40 can be factored:
1x%5E2%2B3x%2B-40+=+1%28x-5%29%2A%28x--8%29
Again, the answer is: 5, -8. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B3%2Ax%2B-40+%29