4. 60 metres of fencing will be used to enclose a rectangular garden. Let 𝑤 be the width of the garden.

Question

a) Find a function 𝐴 in the variable 𝑤 to give the area of the garden. (Hint: You need to find an area function 𝐴(𝑤) which only has the variable width 𝑤. There should not be a variable length 𝑙 in this formula.)

b) Use your formula from part a) to evaluate 𝐴(20). What does this answer represent? Be specific.

Answer 1

width --- w
length --- l
2w + 2l = 60
w+l = 30
l = 30-w

A(w) = wl = w(30-w)
= -w^2 + 30w

a(20) = -400 + 600 = 200

so what do you think ?