Question

Tessa has 80 ft of fencing available to construct a fence that will divide her garden into four equal rectangular sections. Her house forms one side of the garden and 𝑥 represents the width, as shown in Figure 1.

(a) Express the total area of the four sections as a function of x.
Hint: if you call 𝑦 each of the four sections perpendicular to 𝑥, find the perimeter of the fence in terms of 𝑥,𝑦 x,y, then use the fact that the perimeter is 80 ft.

𝐴(𝑥)=

Answer 1

Don't know what the diagram looks like but I assumed
a rectangle against the wall, (one length not needed)
I then split that rectangle into 4 equal rectangles
For a small rectangle , let the width be x and its length by y.
So I will need 6x + 4y = 80
3x + 2y = 40
y = (40-3x)/2

area of whole big one = (2x)(2y) = 4xy
= 4x(40-3x)/2
= 80x - 6x^2

d(area) = 80 - 12x = 0 for a max of area
x = 80/12 = 20/3
then y = (40-3x)/2
= (40 - 20)/2 = 10

state you conclusion