Story problem

Question

A farmer plans to use 180 feet of fencing to enclose a rectangular region, using part of a straight river bank instead of fencing as one side of the rectangle, as shown in the figure.

(a) Find the area A of the region if the length of the side parallel to the river bank is four times the length of an adjacent side.
A =
ft2

(b) Find the area A of the region if the length of the side parallel to the river bank is one-fourth the length of an adjacent side.
A =
ft2

(c) Find the area A of the region if the length of the side parallel to the river bank is the same as the length of an adjacent side.
A =
ft2

Answer 1

Hi Ali.

 

A rectangle's area is:

A = w x h

 

For problem a, we know that w = 4h

Let's rewrite our area formula in terms of h.

A = 4h x h (where h is the short side)

 

The farmer built 180 ft of fence to wrap 2 short sides and 1 long side.

This means the following:
180ft = w + h + h

substitute w with 4h

180ft = 6h

h = 30 feet

 

A = 4h x h = 4(30) x 30 = 3600 sq. ft.

 

Hopefully this will be enough to help you finish up the other 2.

Answer 2

(a)

s represents the length of a side

4s represents the length of the parallel side

 

s + s + 4s = 180

6s = 180

s = 30

 

A = s(4s)

A = 4s²

A = 4(30²)

A = 4(900)

A = 3600

 

(b) and (c) are done the same way.