Find the area: A rectangle with length 12 inscribed in a circle with radius 7.5 (explain how you do it please! Thanks!)
It would help if you proofread your questions before you posted them. What do you want to do/find?
To find the area of the rectangle inscribed in a circle, we need to break down the problem into smaller steps:
Step 1: Determine the dimensions of the rectangle.
Since the rectangle is inscribed in a circle, its diagonal will be equal to the diameter of the circle. In this case, the radius of the circle is given as 7.5. So, the diameter of the circle is 2 * 7.5 = 15.
Step 2: Use the Pythagorean theorem to find the dimensions of the rectangle.
The diagonal of the rectangle splits it into two right-angled triangles. Let's consider one triangle. The hypotenuse is the diagonal of the rectangle, which we found to be 15. Let's assume the length of the rectangle is represented by 'a', and the width of the rectangle is represented by 'b'.
Using the Pythagorean theorem (a^2 + b^2 = c^2), we have:
a^2 + b^2 = 15^2
a^2 + b^2 = 225 -- equation (1)
Step 3: Determine the relationship between the length and width of the rectangle.
We are told that the length of the rectangle is 12. Therefore, we can substitute that value into equation (1):
12^2 + b^2 = 225
144 + b^2 = 225
b^2 = 225 - 144
b^2 = 81
b = √81
b = 9
So, we have found the width of the rectangle to be 9 inches.
Step 4: Calculate the area of the rectangle.
The area of a rectangle is given by the formula: A = Length * Width.
In this case, the length of the rectangle is 12 inches, and the width is 9 inches.
A = 12 * 9
A = 108 square inches.
Therefore, the area of the rectangle inscribed in the circle with a radius of 7.5 inches is 108 square inches.
To find the area of a rectangle inscribed in a circle, we need to understand the relationship between the rectangle and the circle.
In this case, we have a rectangle with a length of 12 inscribed in a circle with a radius of 7.5. It means that the circle touches the four sides of the rectangle.
To compute the area, we need to find the dimensions of the rectangle. As the circle touches the top and bottom sides of the rectangle, the width of the rectangle would be equal to the diameter of the circle, which is twice the radius.
So, the width of the rectangle = 2 * radius = 2 * 7.5 = 15.
The area of the rectangle can be calculated by multiplying the length and width. In this case, the length is given as 12, and the width is 15.
Therefore, the area of the rectangle is:
Area = length * width = 12 * 15 = 180 square inches.
So, the area of the rectangle is 180 square inches.