Question

A gardener has 100 meters of fencing to enclose two adjacent rectangular gardens, as shown in the figure.

Answer 1

Given that the length of the fence is 100=4x+3y, to express the area of the garden as a function of x we proceed as follows;
4x+3y=100
making y the subject we get:
3y=100-4x
y=1/3(100-4x)
therefore the width of the garden is:
y=1/3(100-4x)
hence the area of the fence garden will be:
Area=length*width
length=2x 
width=y=1/3(100-4x)
thus;
A=2x*[1/3(100-4x)]
=2/3[100x-4x^2] square units