Question

In a school, a circular playground has an area of 3x^2-9x. There are two rectangular football fields with dimensions 2x by 5 in the playground. Find the simplified expression for the area excluding the football fields.

Answer 1

Explanation:

To find the simplified expression for the area of the circular playground excluding the football fields, we need to subtract the area of the two rectangular football fields from the total area of the circular playground.

The area of a circle is given by the formula A = πr^2, where r is the radius of the circle.

We are given that the area of the circular playground is 3x^2 - 9x. To find the radius, we need to take the square root of the area divided by π.

Taking the square root of 3x^2 - 9x gives us the radius of the circular playground: √(3x^2 - 9x).

The area of a rectangle is given by the formula A = length × width. In this case, the length is 2x and the width is 5.

Therefore, the area of one rectangular football field is (2x)(5) = 10x.

Since there are two rectangular football fields, the total area of the football fields is 2(10x) = 20x.

To find the area excluding the football fields, we subtract the area of the football fields from the area of the circular playground:

Area excluding football fields = 3x^2 - 9x - 20x.

Simplifying the expression, we have:

Area excluding football fields = 3x^2 - 29x.

Therefore, the simplified expression for the area of the circular playground excluding the football fields is 3x^2 - 29x.

Answer 2

To find the simplified expression for the area of the circular playground excluding the football fields, you first need to find the area of the circular playground and then subtract the combined area of the two rectangular football fields.

Area of the Circular Playground:

The area of a circle with radius "r" is given by the formula A = πr^2.

In your case, the area of the circular playground is given as 3x^2 - 9x. So, you can set this equal to the formula for the area of a circle:

3x^2 - 9x = πr^2

Find the Radius (r):

To find the radius "r," you need to solve for it:

3x^2 - 9x = πr^2

Divide both sides by π:

(3x^2 - 9x) / π = r^2

Take the square root of both sides:

r = √((3x^2 - 9x) / π)

Calculate the Area of the Football Fields:

Each football field has dimensions 2x by 5, so the area of one football field is (2x)(5) = 10x square units. Since there are two football fields, their combined area is 2 * 10x = 20x square units.

Calculate the Area Excluding Football Fields:

Now, subtract the area of the football fields from the area of the circular playground:

Area excluding football fields = (3x^2 - 9x) - 20x

Simplify this expression:

Area excluding football fields = 3x^2 - 9x - 20x

Area excluding football fields = 3x^2 - 29x

So, the simplified expression for the area of the circular playground excluding the football fields is 3x^2 - 29x square units.

Explanation: