Mathematics: 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?

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You are enclosing a rectangular garden with feet

andrewmena05

08.02.2022

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

Step-by-step 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 $= l\times b=200$

$\Rightarrow (30-b)b=200$ [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.

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