A rectangle is inscribed in a semi circle of radius 2, let x represent half the length of the rectangle. Write an expression for the area of the rectangle in terms of x.
Well I know area=length X width. That's about all I know what to do though
r ^ 2 = x ^ 2 + w ^ 2
2 ^ 2 = x ^ 2 + w ^ 2
4 = x ^ 2 + w ^ 2
w ^ 2 = x ^ 2 - 4
w = sqrt ( x ^ 2 - 4 ) =
A = 2 x * w
A = 2 x * sqrt ( x ^ 2 - 4 )
OH! Okay thanks! I was doing something similar, but I guess I was just confusing myself. That was actually pretty simple.
To find the area of the rectangle, we need to determine the length and width of the rectangle in terms of x.
Let's start by visualizing the rectangle inscribed in the semicircle. Given that the radius of the semicircle is 2, we know that the diameter of the semicircle is twice the radius, which is 4.
Since the rectangle is inscribed in the semicircle, the rectangle's length will be equal to the semicircle's diameter, which is 4. Therefore, the length of the rectangle is 2x.
The width of the rectangle will be equal to the radius of the semicircle, which is 2.
Now that we have both the length and width of the rectangle, we can calculate its area. The formula for the area of a rectangle is length multiplied by width.
So, the expression for the area of the rectangle in terms of x can be written as:
Area = length × width
Area = (2x) × 2
Area = 4x
Therefore, the expression for the area of the rectangle in terms of x is 4x.