a possible length

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Fri Mar 04, 2011 2:05 am

Which of the following is a possible length for side AB of triangle ABC if AC = 6 and BC = 9?
I. 3
II. 9 âˆš3
III. 13.5
(A) I only
(B) II only
(C) III only
(D) II and III
(E) I, II, and III

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Source: Beat The GMAT — Problem Solving | Fri Mar 04, 2011 2:05 am

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Fri Mar 04, 2011 2:22 am

sanju09 wrote:Which of the following is a possible length for side AB of triangle ABC if AC = 6 and BC = 9?
I. 3
II. 9 âˆš3
III. 13.5

Length of AB must be within the difference and sum of the lengths of AC and BC, i.e. within 3 and 15 (excluding 3 and 15). Only such option is 13.5.

Hence the correct answer is C.

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Anaira Mitch: Master | Next Rank: 500 Posts; Posts: 235; Joined: Wed Oct 26, 2016 9:21 pmFollowed by: 5 members; Thanked: 3 times

by Anaira Mitch » Fri Dec 30, 2016 2:15 am

The third side of a triangle must be less than the sum of the other two sides and greater than their difference (i.e. |y - z| < x < y + z).
In this question:
|BC - AC| < AB < BC + AC
9 - 6 < AB < 9 + 6
3 < AB < 15
Only 13.5 is in this range. 9sqrt3 is approximately equal to 9(1.7) or 15.3.
The correct answer is C.

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Fri Dec 30, 2016 8:06 am

sanju09 wrote:Which of the following is a possible length for side AB of triangle ABC if AC = 6 and BC = 9?
I. 3
II. 9 âˆš3
III. 13.5
(A) I only
(B) II only
(C) III only
(D) II and III
(E) I, II, and III

IMPORTANT RULE: If two sides of a triangle have lengths A and B, then . . .
DIFFERENCE between sides A and B < third side < SUM of sides A and B

So, based on the rule, we know that: 9-6 < third side < 9+6
In other words, 3 < third side < 15

Now check the 3 statements:
I. 3 - NOT within the range of 3 < third side < 15

II. 9âˆš3 - all students should memorize that âˆš3 â‰ˆ 1.7 (along with âˆš2 â‰ˆ 1.4 and âˆš5 â‰ˆ 2.2)
So 9âˆš3 â‰ˆ 9(1.7) â‰ˆ 15.3. This is NOT within the range of 3 < third side < 15

III. 13.5 WORKS! 13.5 IS within the range of 3 < third side < 15

Answer: C

Brent Hanneson - Creator of GMATPrepNow.com

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8138; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Wed Jan 04, 2017 7:24 am

sanju09 wrote:Which of the following is a possible length for side AB of triangle ABC if AC = 6 and BC = 9?

I. 3
II. 9 âˆš3
III. 13.5

(A) I only
(B) II only
(C) III only
(D) II and III
(E) I, II, and III

This problem is testing us on the triangle inequality theorem in which the sum of the lengths any two sides of a triangle MUST be greater than that of the third side. Let's test each Roman numeral to determine which could be a possible side length of AB. Keep in mind that AC = 6 and BC = 9.

I. 3

Since 6 + 3 IS NOT greater than 9, 3 cannot be the length of side AB.

II. 9âˆš3

9âˆš3 is roughly equal to 9 x 1.7 = 15.3, and since 6 + 9 IS NOT greater than 15.3, 9âˆš3 cannot be the length of side AB.

III. 13.5

Since 6 + 13.5 IS greater than 9, 13.5 + 9 IS greater than 6, and 9 + 6 IS greater than 13.5; thus, 13.5 could be the length of side AB.

Answer: C

Scott Woodbury-Stewart
Founder and CEO
[email protected]

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