Problema Solution
hank has 20 yards of lumber that he can use to build a raised garden. write and graph a linear inequality that describes the possible lengths and widths of the garden. if hank wants he demensions to be whole numbers only, what demensions would produce the largest area?
Answer provided by our tutors
let
l = the length of the garden
w = the width of the garden
the perimeter of the garden should be not bigger then 20 yards
2(l + w) <= 20 divide both sides by 10
l + w <= 10
click here to see the graph
the possible values for l and w can be easily noted from the graph
hank wants he dimensions to be whole numbers only thus l and w needs to be integers
the area of the garden will be A = l*w
we need to find l and w such that l>0, w > 0, l + w<=10, l and w are integers
we know that the biggest area of rectangle is achieved when the rectangle is square that is l = w thus for l = w = 5 yd will provide the biggest area A = 25 yd^2.