perimeter ?

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govind_raj_76: Senior | Next Rank: 100 Posts; Posts: 32; Joined: Tue Apr 20, 2010 7:16 pm; Location: Newark, DE

perimeter ?

by govind_raj_76 » Sat Apr 24, 2010 10:11 am

If the perimeter of an isosceles triangle is 50. Which of the following CANNOT be the length of a side of the traiangle ?

a) 15
b) 18
c) 20
d) 24
e) 26

Please let me know how to solve this ?

Govind

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Source: Beat The GMAT — Problem Solving | Sat Apr 24, 2010 10:11 am

iamseer: Master | Next Rank: 500 Posts; Posts: 170; Joined: Wed Jun 10, 2009 5:59 am; Thanked: 13 times

by iamseer » Sat Apr 24, 2010 10:30 am

clearly E

since it is an isosceles triangle sides are x,x,y
therefore 2x+y=50

now 26,26, y is obviously not possible
also x,x, 26 means x=12: is not possible b'cos sum of length of any 2 sides of a traingle must be greater than length 3rd side

"Choose to chance the rapids and dance the tides"

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rn4gmat: Junior | Next Rank: 30 Posts; Posts: 16; Joined: Sun Apr 18, 2010 7:44 pm; Thanked: 3 times

by rn4gmat » Sat Apr 24, 2010 10:32 am

In a triangle the length of the any side cannot be greater then the sum of the other 2 sides.
Also it is given that the given triangle is an isosceles triangle so the answer to this would be E.
The length of any side cannot be 26.

Hope this helps.

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frank1: Legendary Member; Posts: 537; Joined: Fri Jan 22, 2010 10:06 pm; Thanked: 14 times; Followed by:1 members

by frank1 » Sat Apr 24, 2010 10:35 am

E and i used backward solving
larger the third value smaller will be other 2 values....(smaller the other 2 values impossible to make triangle)
so took 26, if 3rd side is 26
then remaining sides are 12 and 12
12+12=24 (triangle cannot be drawn)
done
26+26 is not possible either

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govind_raj_76: Senior | Next Rank: 100 Posts; Posts: 32; Joined: Tue Apr 20, 2010 7:16 pm; Location: Newark, DE

by govind_raj_76 » Sat Apr 24, 2010 2:27 pm

What about 24 and 20 ?

a) with 24

2x+y=50,
x=24,x=24, y=2

Even 24,24 and 2 is not possible right ??
also if y=24, x,x, 24 means x=13: is not possible b'cos sum of length of any 2 sides of a traingle must be greater than length 3rd side.

24 +13 greater than 13.
13+13 NOT greater than 24. Even in this case triangle is not possible right ??

b) with 20

2x+y=50, x=20, x=20, y=10
20+10 > 20

if y=20, x=15, x,x, 20 means x=15,

15+15 > 20,
15 + 20 > 15.

It looks like the triangle is NOT possible with a) with 24 and looks possible with b) 20.

Why did we pick 26 and not 24 ? Please help..

Govind

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frank1: Legendary Member; Posts: 537; Joined: Fri Jan 22, 2010 10:06 pm; Thanked: 14 times; Followed by:1 members

by frank1 » Sat Apr 24, 2010 7:00 pm

govind_raj_76 wrote:What about 24 and 20 ?

a) with 24

2x+y=50,
x=24,x=24, y=2

Even 24,24 and 2 is not possible right ??

Why did we pick 26 and not 24 ? Please help..

how
side 24 24 2
24+2>24
24+24>2

so it is possible...why are you saying it is not possible?

with 26 it is not possible...
i have taken 26 as an educated guess as explained above

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eliazashin: GMAT Instructor; Posts: 18; Joined: Wed Jan 13, 2010 11:35 pm; Location: Austin, Texas; Thanked: 4 times; Followed by:1 members; GMAT Score:750

by eliazashin » Sat Apr 24, 2010 7:17 pm

Hey All, Given the language of the question presented, the answer is (E). Those who said to use the 3rd side rule are correct!

Keep it up, mathematicians!

Elia
GMAT Trainer, The Princeton Review

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frank1: Legendary Member; Posts: 537; Joined: Fri Jan 22, 2010 10:06 pm; Thanked: 14 times; Followed by:1 members

by frank1 » Sat Apr 24, 2010 7:36 pm

eliazashin wrote: Keep it up, mathematicians!

thanks sir,i wish i were able to be one....lol (i am programmer by the way)

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eliazashin: GMAT Instructor; Posts: 18; Joined: Wed Jan 13, 2010 11:35 pm; Location: Austin, Texas; Thanked: 4 times; Followed by:1 members; GMAT Score:750