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sana.noor: Legendary Member; Posts: 512; Joined: Mon Jun 18, 2012 11:31 pmFollowed by: 20 members; Thanked: 42 times

by sana.noor » Tue Jul 09, 2013 5:54 am

Triangle ABC and Triangle CDF has angle a = angle c , angle d = angle b and angle c = angle f. the area of triangle cdf is twice the area of triangle ABC. if the base of triangle ABC is s,and the base of triangle CDF is S, then in terms of s, S =

1. sqrt(2)/2 s
2. sqrt(3)/2 s
3. sqrt(2)s
4. sqrt(3)s
5. 2s

OA is 3

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Source: Beat The GMAT — Problem Solving | Tue Jul 09, 2013 5:54 am

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by [email protected] » Tue Jul 09, 2013 11:59 am

Hi sana.noor,

This question is a high-level multi-shape geometry question that involves similar triangles. It's rare and usually worth very little (or nothing) to your overall Quant score. To solve it, try using the Empowergmat tactic TEST IT:

First draw a triangle (you'll find using a right triangle to be easiest). Now, pick a base and a height.

As an example, pick a base of 4 and a height of 3. It's area = .5(4)(3) = 6

Since the second triangle has the SAME ANGLES and an area that's twice as big, it's area = 12

So you have to go from an area of 6 to an area of 12 AND use similar triangles (which means that the side lengths of the big triangle are all proportionately bigger than the smaller triangle).

This means that the base(root2) x height(root2) would account for the "double area"

If the base of the small triangle is s, then the base of the big triangle would be s(root2).

Final Answer C

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Tue Jul 09, 2013 1:42 pm

Check here for my solution to a very similar problem from GMAT Prep:

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faraz_jeddah: Master | Next Rank: 500 Posts; Posts: 358; Joined: Thu Apr 18, 2013 9:46 amFollowed by: 7 members; Location: Jeddah, Saudi Arabia; Thanked: 42 times; GMAT Score:730

by faraz_jeddah » Wed Jul 10, 2013 2:24 pm

[email protected] wrote:Hi sana.noor,

This question is a high-level multi-shape geometry question that involves similar triangles. It's rare and usually worth very little (or nothing) to your overall Quant score.
Rich

Hi Rich. Out of curiosity, where did you find that information?

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[email protected]: Newbie | Next Rank: 10 Posts; Posts: 4; Joined: Sat Jun 23, 2012 11:16 am

by [email protected] » Fri Jul 12, 2013 10:42 am

sana.noor wrote:Triangle ABC and Triangle CDF has angle a = angle c , angle d = angle b and angle c = angle f. the area of triangle cdf is twice the area of triangle ABC. if the base of triangle ABC is s,and the base of triangle CDF is S, then in terms of s, S =

1. sqrt(2)/2 s
2. sqrt(3)/2 s
3. sqrt(2)s
4. sqrt(3)s
5. 2s

OA is 3

An alternate way is to use the property of Similar Triangles and their corresponding areas.

ie if we know the similarity ratio, we can square this ratio to determine ratio of the triangles' areas.

In this case:

Step 1) s/S is the Similarity Ratio.

Step 2) Take the Square of the Similarity Ratio ie (s/S)^2

Step 3) Equate the above value to the ratio of the Areas of Triangles ie (s/S)^2 = 1/2

Solving this Equation we get S= sqrt(2)s.

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