SOLUTION: The height of a bookcase is 3 feet longer than the length of a shelf. If 18 feet of lumber is available for the entire unit, find the length and height of the unit. HELP PLEASE

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Question 104684: The height of a bookcase is 3 feet longer than the length of a shelf. If 18 feet of lumber is available for the entire unit, find the length and height of the unit.
HELP PLEASE
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
let the height be a, and the length b
The height of a bookcase is 3ft longer than the length+of a shelf.
so, we can write:
a+=+b%2B+3ft
or
b=+a+-+3ft
If 18 feet of lumber is available for the entire unit, the perimeter is 18ft
if perimeter is P,
P+=+2%28a+%2B+b%29
18ft+=+2%28+a+%2B+b+-+3ft%29 we can divide both sides by 2, and we will have
9+ft=+2a+-+3ft
2a+=+9+%2B+3ft
2a=+12ft divide both sides by 2

a+=+6ft
then
b+=+a+-+3ft
b=+3ft