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There is a rectangular parking lot with a length of 2x and a width of x. if the ratio of the perimeter of the parking lot to the area of the parking lot is given by $k x$ , then find the value of k.

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answer is C.

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Detailed Solution

We are given that the length of the rectangular parking lot is 2x, i.e.

We also have the width of the parking lot x. Let's label it as

It is given that the ratio of the perimeter to the area of the parking lot =

⇒ Perimeter of parking lot Area of parking lot = k x ... (i)

First, we find the perimeter of the given rectangular parking lot.
We know that the perimeter of a rectangle

We substitute the values. we will get
Perimeter of Parking area

Now we find the area of the parking lot.
We know the area of the rectangle

Substituting the values, we get
Area of Parking area

Now we replace them in (i)

⇒ 6 x 2 x 2 = k x

⇒ 6 2 x = k x

6 x = 2 x k

6 = 2 k

⇒ 2 k = 6 ⇒ k = 3

Hence, the value of k is 3.
So, the correct answer is Option 3.

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