Quadratic Equation

Question

Rahim suggests to fence up two adjacent pieces of rectangular land as shown above to plant flowers. He has a wire fence of 24 m length.

(a) Find total area of the land, A m², in terms of x.

(b) Find

i) the value of x and the value of y, such that

the area A is a maximum.

ii) the maximum area, in m².

Answer 1

Draw and label a diagram!

x represents the length of the pen

y represents the length of the dividing fences

3y + 2x = 24

3y = 24 - 2x

y = 8 - 2x/3

A = xy

A = x(8 - 2x/3)

A = 8x - 2x² / 3

Maximum at x = -8 / (2)(-2/3), or x = 6

y = 4, Area is 24 ft²