SOLUTION: A bookcase is to be constructed as shown in the figure below. The height of the bookcase is 3 feet longer than the length of a shelf. If 18 feet of lumber is available for the enti

Algebra ->  Equations -> SOLUTION: A bookcase is to be constructed as shown in the figure below. The height of the bookcase is 3 feet longer than the length of a shelf. If 18 feet of lumber is available for the enti      Log On


   

Question 1086531: A bookcase is to be constructed as shown in the figure below. The height of the bookcase is 3 feet longer than the length of a shelf. If 18 feet of lumber is available for the entire unit (including the shelves, but NOT the back of the bookcase), find the length and height of the unit.
Answer by mathmate(429) About Me  (Show Source):
You can put this solution on YOUR website!
Question:
A bookcase is to be constructed as shown in the figure below. The height of the bookcase is 3 feet longer than the length of a shelf. If 18 feet of lumber is available for the entire unit (including the shelves, but NOT the back of the bookcase), find the length and height of the unit.

Solution:
Let
L=length in feet
then
H=L+3 ft
Perimeter=18'

Set up equation for perimeter
Perimeter = 18 = 2(L+H) = 2(L+L+3) = 2(2L_+3) =4L+6
Solve for L:
4L+6=18
subtract 6 from both sides
4L=18-6=12
L=3
H=3+3=6

Answer: Length (i.e. width of bookcase) = 3'; Height = 6'