Question 1086531
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'