geometry problem

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ern5231: Master | Next Rank: 500 Posts; Posts: 226; Joined: Sun Aug 09, 2009 4:34 am

by ern5231 » Sat Sep 26, 2009 7:53 am

21) Triangle ABC is an equilateral triangle with CD perpendicular to AB. E is a point on CD in which DE=AD=a. What is the perimeter of ACE in terms of a?

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truplayer256: Master | Next Rank: 500 Posts; Posts: 392; Joined: Thu Jan 15, 2009 12:52 pm; Location: New Jersey; Thanked: 76 times

by truplayer256 » Sat Sep 26, 2009 8:06 am

asqrt(3)-a+asqrt(2)+2a or asqrt(3)+asqrt(2)+a.

If that's the correct answer, please let me know and I'll explain.

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ssmiles08: Master | Next Rank: 500 Posts; Posts: 472; Joined: Sun Mar 29, 2009 6:54 pm; Thanked: 56 times

by ssmiles08 » Sat Sep 26, 2009 9:35 am

I got asqrt(3) + asqrt(2) + a

DA = a
AD = a

traingle ADE would be a 90-45-45 triangle. so AE = asqrt(2)

Line CD bisects AB so since ABC is an equilateral triangle, AC = 2a.

Line CD = asqrt(3) since triangle ADC is a 30-60-90 triangle.

CD = asqrt(3) ED = a so CE = asqrt(3) - a

triangle ACE = aqrt(3) - a + asqrt(2) + 2a

asqrt(3) +asqrt(2) + a

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fruti_yum: Master | Next Rank: 500 Posts; Posts: 128; Joined: Thu Jul 30, 2009 1:46 pm; Thanked: 1 times

by fruti_yum » Wed Sep 30, 2009 9:34 am

ssmiles08 wrote:I got asqrt(3) + asqrt(2) + a

DA = a
AD = a

traingle ADE would be a 90-45-45 triangle. so AE = asqrt(2)

Line CD bisects AB so since ABC is an equilateral triangle, AC = 2a.

Line CD = asqrt(3) since triangle ADC is a 30-60-90 triangle.

CD = asqrt(3) ED = a so CE = asqrt(3) - a

triangle ACE = aqrt(3) - a + asqrt(2) + 2a

asqrt(3) +asqrt(2) + a

How can you just assume Line CD bisects AB?? It only said it forms a 90 degree angle!.. doesn't say ad= ab? anywhere?

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xcusemeplz2009: Master | Next Rank: 500 Posts; Posts: 399; Joined: Wed Apr 15, 2009 3:48 am; Location: india; Thanked: 39 times

by xcusemeplz2009 » Wed Sep 30, 2009 9:58 am

fruti_yum wrote:
ssmiles08 wrote:I got asqrt(3) + asqrt(2) + a

DA = a
AD = a

traingle ADE would be a 90-45-45 triangle. so AE = asqrt(2)

Line CD bisects AB so since ABC is an equilateral triangle, AC = 2a.

Line CD = asqrt(3) since triangle ADC is a 30-60-90 triangle.

CD = asqrt(3) ED = a so CE = asqrt(3) - a

triangle ACE = aqrt(3) - a + asqrt(2) + 2a

asqrt(3) +asqrt(2) + a
How can you just assume Line CD bisects AB?? It only said it forms a 90 degree angle!.. doesn't say ad= ab? anywhere?

in an equilateral triangle a perpendicular drawn from a vertex to a side will bisect the side and h=sqrt3/2*(side).[theorem]

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