Question

PLEASE HELP
WILL FAN AND MEDAL

In the figure above , OACB is a square with area 4x^2. If OA and OB are radii of a sector of a circle O, what is the perimeter, in terms of x, of the unbroken figure?

A) x(4+3 π)
B) x(3+4π)
C) x(6+4 π)
D) 4(x+2 π)
E) 7 πx

Answer 1

please help!

Answer 2

OACB is a square with area of 4x^2 , so each side is 2x.
And the side of the square is equal to the radius of the circle, then the radius is 2x too.
Now, we'll calculate the perimeter in 2 steps, step 1 is calculating the perimeter of arc BA (counterclockwise) that is 3/4 of the total perimeter of the circle, and by the formula of the perimeter of a circle
\[2\pi \times radius\]
we calculate:
\[2\pi \times2x=4pix\]
but arc BA is 3/4 of the perimeter of the circle, then
\[4pix \times \frac{ 3 }{ 4 }=3pix\] so the perimeter of BA is
\[3pix\]
now, the step 2, calculating BC + CA, and BC=CA=OA=OB (because is a square) the BC + CA= 2BC, and BC=2x, then 2BC=4x.
After all this we sum
\[4x+3pix\]
factoring by x we get
\[x(4+3\pi)\]
Alternative A

Answer 3

ah i see
thanks!