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What is the perimeter of the figure?

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by AAPL » Sun Nov 26, 2017 8:54 am
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In the figure above, triangle CDE is an equilateral triangle with side length 3, AF=10, EF=6 and AB=DE. What is the perimeter of the figure?

(A) 45
(B) 36
(C) 29
(D) 24
(E) 16

The OA is C.

Please, can any expert assist me with this PS question? I don't have it clear and I appreciate if any explain it for me. Thanks.
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Source: — Problem Solving |

by [email protected] » Sun Nov 26, 2017 9:59 am
Hi AAPL,

While we're given a lot of information to work with, this question is mostly about recognizing the 'classic' right triangles involved and staying organized with how the various 'side lengths' relate to one another. To find the perimeter, we need to define the 'outside lines' of the shape.

-Since AF=10 and EF=6, we have a 3/4/5 right triangle that's been 'doubled', so AE = 8
-CDE is an EQUILATERAL triangle with sides of 3, so AC = 5
-AB = DE = 3 and triangle ABC is a 3/4/5 right triangle, so BC = 4

Now you have all of the perimeter side lengths: 3+4+3+3+6+10 = 29

Final Answer: C

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Rich
Contact Rich at [email protected]
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