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The volume of a box like this is found by multiplying the length times the width times the height. We are told that the length is 8 more inches than the width, so the width is w and the length is w + 8. If we cut away 3 square inches from each corner, the height when we fold up those corners is going to be 3. The volume is given as 27, so our formula looks like this: 
. When we do that multiplication, we have 
. We need to solve for w so we can then solve for h. Move the 27 over and set the quadratic equal to 0. 
. We can then factor out a 3 to make the job easier: 
. Now we can factor to solve for w. The 2 numbers that add up to 8 and multiply to -9 are 9 and -1. So (w+9) = 0, (w-1) = 0, or 3 = 0. Of course 3 doesn't equal 0, so that's out. w + 9 = 0 so w = -9. w - 1 = 0 so w = 1. There are 2 things in math that can never EVER be negative and those are time and distance/length. So -9 is out. That means that w = 1. But don't forget that there was 6 inches cut off each side, so the width is 1 + 3 + 3 which is 7. The length is w + 8 which means that the length is 7 + 8 or 15. Those are the dimensions of the rectangle before it was cut.
Answer:
The new ramp must be 54 inches long than the old ramp to meet the requirement of the new law
Step-by-step explanation:
Old height to length ratio is:
h : l = 2 : 15.
Height of old ramp h = 12
Length of old ramp can be find out by putting h = 12 in the above ratio
Length of old ramp = 90
Height to length ratio by current law:
h : l = 1 : 12
Height will be the same i.e. h = 12
Length of new ramp = 144
How much longer the new ramp should be to meet the new ratio law:
New length - Old length = 144 - 90 = 54 inches