SOLUTION: A rectangular instrument case has an are of 40in^2. if the length is 6in. more than the width, find the dimensions of the length. (A=L*W)

Question 248260: A rectangular instrument case has an are of 40in^2. if the length is 6in. more than the width, find the dimensions of the length. (A=L*W)
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
40=L*W
L=6+W
substitute 6+w for L in 40=L*W to get 40=(6+W)*W
40=(6+W)*W
40=6W+W^2
subtract 40 from both sides and move everything to the opposite sides
W^2+6W-40=0
to factor we need factors of 40 that are different by 6
factors of 40
40*1;20*2;10*4;5*8
which ones are different by 6
10 and 4
we need positive six so we need 10-4
(x-4)(x+10)=0
x=4 and x=-10

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=196 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 4, -10. Here's your graph:

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