Question

the perimeter of a rectangular campsite is 64m and its area is 207m^2. find the length and breadth of the campsite

Answer 1

The length is
`23\ m` and the breadth is
`9\ m`

Explanation:

Let

x ----> the length of a rectangular campsite

y ----> the breadth of a rectangular campsite

we know that

The perimeter of a rectangle is equal to

`P=2(x+y)`

`P=64\ m`

so

`64=2(x+y)`

`32=(x+y)`

`y=32-x` ------> equation A

The area of a rectangle is equal to

`A=xy`

`A=207\ m^(2)`

so

`207=xy` -----> equation B

substitute equation A in equation B

`207=x(32-x)\\\\207=32x-x^(2)\\\\x^(2)-32x+207=0`

Solve the quadratic equation by graphing

The solution is
`x=23\ m` ( I assume that the length is greater than the breadth)

see the attached figure

Find the value of y

`y=32-23=9\ m`

therefore

The length is
`23\ m` and the breadth is
`9\ m`