If there are 80 feet of wood to use to build the set of shelves what should the dimensions of the set of shelves be?

Question

2. The width of the set of shelves needs to be 5 times the height of the set of shelves and the set of shelves must have three shelves in it.  If there are 80 feet of wood to use to build the set of shelves what should the dimensions of the set of shelves be?

 

Answer 1

From my understanding of the question, the following is my answer.

Let width and height of the shelves be w and h respectively.

Given, w = 5h  ------------------(1)

and perimeter of the shelves = 2(w+h)

but there are 2 extra wooden brackets so that the set of shelves contains 3 shelves

So the total wood = perimeter of the set of shelves + width 2 extra wooden brackets

So, 80 = 2(w+h) +2w

or 80  =4w +2h

or 80 = 4(5h) +2h

or 80 = 22h

or h = 80/22 = 40/11

Putting the value of h in eq(1) we get:

w = 200/11

So the width of the set of shelves should be 200/11 feet and its height should be 40/11 feet