frustrating geometry question

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<p>The flag shown above is made of overlapping equilateral triangles ADF and BCE. If CD, DE and EF each have length 10 inches, what is the perimeter of the flag? (grid-in question)</p>

<p>Is the answer 110?</p>

<p>^I think it’s 90</p>

<p>Ahhh I think you’re right. I didn’t realize they were overlapped.</p>

<p>They’re equilateral triangles, meaning all sides are equal. Triangle EBC’s bottom side is CD + DE, which is 10 + 10, which is 20, so all its sides are 20 (sides BC, BE and EC). The same goes for triangle ADF (all sides are 20 since bottom is DE + EF, which is 10 + 10, which is 20, and since it’s an equilateral triangle all sides are 20, meaning sides AF, AD and FD). Obviously the smaller triangle in the middle has all sides equal to 10. Let x = the point at the top of the smaller triangle with side DE. Therefore, sides Dx, Ex and DE are all 10 (equilateral triangle)</p>

<p>Base of flag: CD + DE + EF = 10 + 10 + 10 = 30
Sides of flag: AF + BC = 20 + 20 = 40
Inner Parts of Flag: Bx + Ax = 10 + 10 = 20</p>

<p>Perimeter = Base + Sides + Inner Parts = 30 + 40 + 20 = 90</p>

<p>Question already answered here: <a href=“http://talk.collegeconfidential.com/1064667591-post42.html[/url]”>http://talk.collegeconfidential.com/1064667591-post42.html&lt;/a&gt;&lt;/p&gt;

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<p>How did you come to that conclusion? I’m still wondering how to ascertain that BD and DE bisect each other.</p>

<p>“How did you come to that conclusion? I’m still wondering how to ascertain that BD and DE bisect each other.” </p>

<p>Good question…Notice that the bottom right angle of the big equilateral triangle to the left must be 60 degrees (all angles of an equilateral triangle are equal, meaning all three angles are 60 degrees), and this angle comprises one of the angles of the smaller triangle. Now also notice that the bottom left angle of the big equilateral triangle to the right must be 60 degrees, which compromises another angle of the smaller triangle. Therefore, the angles of the small triangle are 60, 60, and 180 - (60 + 60), which is 60. Since all angles are equal it is equilateral, and all sides are 10.</p>

<p>^Nah, I still don’t get it. I mean what you said proves that the small triangle is equilateral. But the triangle could have sides equal to 11 each and still be equilateral. So we need to figure out a geometry rule that says BD and DE bisect each other. :(</p>

<p>WAIT! I just got it! lol…We know that DE=10 and the triangle with base-DE is equilateral. haha</p>