Dimensions

Question

An Architect designs a rectangular flower garden such that the width is exactly two thirds of the length. If 250 feet of fencing are to be used to enclose the garden, find the dimensions of the garden. 

Answer 1

Let's assign the following...

 

L=x.............length of rectangle, given

W=(2/3)x....width of rectangle, given

 

          P=2(L+W)..........perimeter of a rectangle

      250=2[x+(2/3)x]...substitute for "L and W"

      250=2x+(4/3)/x....distribute

      250=(6/3)x+(4/3)x

      250=(10/3)x

(10/3)x=250...............rewrite, variable on LHS

      10x=750...............multiply both sides by 3

          x=75.................divide both sides by 10

 

Let's substitute our calculated "x=75" value back into our "L and W" value assignments earlier...

L = x = 75ft

W=(2/3)x=(2/3)(75)=50ft

 

So the garden dimensions are 75ft by 50ft.  

Let's check our work using the rectangular perimeter formula...

 

P=2(L+W)...........total perimeter of a rectangle

250=2(75+50)...substitute for "L, W and P"

250=2(125).......simplify

250=250............true, √check, calculate values

                            are correct.

 

Always check your solutions and work!