Question

The volume of the cage must be 64m^3. the width to be 4 meters and the height of the cage to be 6 meters less than the length if the other side of the cage. L= and H=

Answer 1

L*W*H=64
we are told that W=4, so
L*4*H=64 (we will come back to this to find H)
the height is 6 less than the Length translates to H=L-6, so
L*4*(L-6)=64
which simplifies to
4L^2-24L=64
subtract 64 from both sides
4L^2-24L-64=0
dividing by 4
4L^2-24L-64=0
L^2-6L-16=0
factoring
(L-8)(L+2)=0
setting each factor to 0 and solving
L=8 or L=-2
so, L=8
To get H, substitute this result into the equation above L*4*H=64:
8*4*H=64
32H=64
H=2
Answer: L=8; H=2

Check:
L*W*H=64
8*4*2=32*2=64

Answer 2

Thank you so much I've been stuck on this for awhile. It turns out the way I was going about it was wrong.

Answer 3

You are welcome!