SOLUTION: please explain me in rectangle the length is one more than breadth, the area is 72sq.units what is the lenth

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Question 687530: please explain me in rectangle the length is one more than breadth, the area is 72sq.units what is the lenth
Answer by Stitch(470) About Me  (Show Source):
You can put this solution on YOUR website!
Area = Length * Breadth
A = L * B
And we know that L = B + 1
And that the area is 72
Rewrite the area equation:
72 = L * B
Substitute (B+1) in for L
72 = (B + 1) * B
Simplify
72 = B^2 + B
Set the equation equal to zero
0+=+B%5E2+%2B+B+-+72
Now you can use the quadratic equation.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation aB%5E2%2BbB%2Bc=0 (in our case 1B%5E2%2B1B%2B-72+=+0) has the following solutons:

B%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=%281%29%5E2-4%2A1%2A-72=289.

Discriminant d=289 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-1%2B-sqrt%28+289+%29%29%2F2%5Ca.

B%5B1%5D+=+%28-%281%29%2Bsqrt%28+289+%29%29%2F2%5C1+=+8
B%5B2%5D+=+%28-%281%29-sqrt%28+289+%29%29%2F2%5C1+=+-9

Quadratic expression 1B%5E2%2B1B%2B-72 can be factored:
1B%5E2%2B1B%2B-72+=+1%28B-8%29%2A%28B--9%29
Again, the answer is: 8, -9. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B1%2Ax%2B-72+%29

Note that you can not have a negative value for the answer. So B = 8
Now plug 8 in for B in the L = B + 1 equation
L = 8 + 1
highlight%28L+=+9%29