BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

As shown in figure, segment AC and segment BD are...

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Moderator
Posts: 2599
Joined: Sun Oct 29, 2017 2:08 pm
Followed by:2 members

As shown in figure, segment AC and segment BD are...

by AAPL » Sun Jan 28, 2018 2:43 pm
As shown in figure, segment AC and segment BD are perpendicular bisector to each other at point O. If OA = OB = 4, perimeter of the shaded region would be?
Image
$$A.\ 2\pi+16$$
$$B.\ 3\pi+24$$
$$C.\ 4\pi+12$$
$$D.\ 4\pi+16$$
$$E.\ 4\pi+20$$

The OA is D.

I don't have clear this PS question.

Can I say that the radius of the semicircular regions are 4, then I have 2/4th parts or 1/2 circumference, I just need to determine the perimeter of this semi-circumference, right?
$$P_{sc}=2r+\pi r\ ?$$
I appreciate if any expert explain it for me. Thank you so much.
Top
Source: — Problem Solving |
Moderator
Posts: 2058
Joined: Sun Oct 29, 2017 4:24 am
Thanked: 1 times
Followed by:5 members

by M7MBA » Mon Jan 29, 2018 2:27 am
Hi AAPL.

Let's see your question.

Your explanation is ok. That is the way to solve this PS question. Another way (almost the same):

We have to calculate $$P=OA+OB+OC+OD+ARC\left(AB\right)+ARC\left(CD\right).$$ We know that OA=OB=OC=OD=4. On the other hand: $$ARC\left(AB\right)=ARC\left(CD\right)=r\cdot\theta=4\cdot\frac{\pi}{2}=2\pi.$$ Therefore, $$P=OA+OB+OC+OD+ARC\left(AB\right)+ARC\left(CD\right)$$ $$=4+4+4+4+2\pi+2\pi\ =\ 16+4\pi.$$ Hence, the correct answer is the option D.

I hope this answer can help you.

I'm available if you'd like a follow-up.

Regards.
Top
Post new topic Post Reply
• Page 1 of 1