SOLUTION: If the volume of a box is 60ft^3, the width is 3ft, the height is 6 more than the length, what is the length? I have been trying this for HOURS.

Question 944408: If the volume of a box is 60ft^3, the width is 3ft, the height is 6 more than the length, what is the length? I have been trying this for HOURS.
Found 2 solutions by Alan3354, macston:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Vol = L*W*H = 60
3*L*(L + 6) = 60
L*(L + 6) = 20
L^2 + 6L - 20 = 0
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Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

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=116 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 2.3851648071345, -8.3851648071345. Here's your graph:

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L =~ 2.385 ft
Answer by macston(5194) (Show Source): You can put this solution on YOUR website!
V=L*W*H
60 cu ft=L*3*(L+6) Divide each side by 3 ft
20 sq ft=L*(L+6)
Subtract 20 sq ft from each side

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=116 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 2.3851648071345, -8.3851648071345. Here's your graph:

Answers 2.385, -8.385 ANSWER L=2.385 (the other answer reverses L and H)
60 cu ft = (2.385 ft)(3 ft)H
60 cu ft=7.155H sq ft divide each side by 7.155 sq ft
8.386 ft=H
CHECK
60 cu ft=L*W*H
60 cu ft=(2.385 ft)(3 ft)(8.386 ft)
60 cu ft=60 cu ft

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