## anonymous one year ago 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

1. anonymous

2. anonymous

3. anonymous

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

4. anonymous

ah i see thanks!