Question

Gerald purchases a rectangular plot of land.The length of the plot is 20 feet more thanthe width. The cost of the land was $12 persquare foot. Gerald also had a fence putaround the entire perimeter of the plot, at acost of $8 per linear foot. The total amounthe spent on both the land and the fence was$10,560What are the dimensions, in feet, of the plot?Provide evidence, including an explanation ofeach step in the solution to the quadraticequation, to support your answer.

Answer 1

Given that,

Gerald purchases a rectangular plot of land.

The length of the plot is 20 feet more than the width.

Let l and w be the length and width of the rectangle respectively in feet.

we get, l=w+20

The cost of the land was $12 per square foot. Gerald also had a fence put around the entire perimeter of the plot, at a cost of $8 per linear foot.

The total amount he spent on both the land and the fence was $10,560

we get,

`12*(l* w)+8(2*(l+w))=10560`

Substitute l, we get,

`12w(w+20)+16(w+20+w)=10560`
`12w^2+240w+32w+320=10560`
`12w^2+272w-10240=0`
`3w^2+68w-2560=0`
`3w^2-60w+128w-2560=0`
`3w(w-20)+128(w-20)=0`

we get,

`(3w+128)(w-20)=0`

The possible width of the rectangle is 20 feet.

Length of the width is 40 feet.

The required dimension of the rectangle is ,

Length is 40 feet and width is 20 feet.