Question

You are enclosing a rectangular garden with feet of ornamental fencing. The area of the garden is square feet. What are the dimensions of the​ garden?

Answer 1

The length and width of the rectangular garden are 20 feet and 10 feet.

Explanation:

Given that the length of fencing = 60 feet

The area of the garden = 200 sq. feet.

As the length of the fencing is equal to the perimeter of the garden, so the perimeter of the rectangular garden is 60 feet.

Let l and b be the length and width of the rectangular garden.

So, the perimeter of the garden = 2(l+b)=60

`\Rightarrow l+b=60/2=30`

`\Rightarrow l=30-b\cdots(i)`

The area of the rectangular garden
`= l* b=200`

`\Rightarrow (30-b)b=200` [from equation (i)]

`\Rightarrow 30b-b^2=200`

`\Rightarrow b^2-30b+200=0`

`\Rightarrow b^2-10b-20b+200=0`

`\Rightarrow b(b-10)-20(b-10)=0`

`\Rightarrow (b-20)(b-10)=0`

`\Rightarrow b-20=0 \;or\; b-10=0`

`\Rightarrow b= 20\;or\; 10`

Now, from equation (i),

If b=20 than l= 30-20=10

or if b=10 than l=30-10=20.

Hence, the length and width of the rectangular garden are 20 feet and 10 feet.