Geometry concepts - Similar triangle problems - The Beat The GMAT Forum

Geometry concepts - Similar triangle problems

Expert replies

sumanr84: Legendary Member; Posts: 758; Joined: Sat Aug 29, 2009 9:32 pmFollowed by: 2 members; Location: Bangalore,India; Thanked: 67 times

by sumanr84 » Tue Jul 27, 2010 11:30 pm

1. The perimeters of two similar triangles is in the ratio 3 : 4. The sum of their areas is 75 cm2. Find the area of each triangle.

2. The areas of two similar triangles are 45 cm2 and 80 cm2. The sum of their perimeters is 35 cm. Find the perimeter of each triangle.

Read more: https://www.cliffsnotes.com/study_guide/ ... z0uxOUeYac

Like this post

Source: Beat The GMAT — Problem Solving | Tue Jul 27, 2010 11:30 pm

GMAT/MBA Expert

Rahul@gurome: GMAT Instructor; Posts: 1179; Joined: Sun Apr 11, 2010 9:07 pmFollowed by: 88 members; Location: Milpitas, CA; Thanked: 447 times

by Rahul@gurome » Tue Jul 27, 2010 11:44 pm

Solution to first question.
Let the sides of one triangle be a, b and c and the ratio of the sides of two triangles be 1:k.
So the sides of other triangle are ka, kb and kc.
Perimeter of first triangle is a+b+c.
Perimeter of second triangle is k(a+b+c).
So (a+b+c):k(a+b+c) = 3:4.
Or k is 4/3.
So the sides are also in the ratio 3:4.
So areas are in the ratio 3^2 : 4^2 which is 9:16.
Or the areas are (9/25)*75 = 27 and (16/25)*75 = 48.

So areas are 27 and 48.

Rahul Lakhani
Quant Expert
Gurome, Inc.
https://www.GuroMe.com
On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
1-800-566-4043 (USA)
+91-99201 32411 (India)

Like this post

GMAT/MBA Expert

Rahul@gurome: GMAT Instructor; Posts: 1179; Joined: Sun Apr 11, 2010 9:07 pmFollowed by: 88 members; Location: Milpitas, CA; Thanked: 447 times

by Rahul@gurome » Tue Jul 27, 2010 11:53 pm

Solution to second question:
Ratio of areas is 45:80 = 9:16.
Or sides are in the ratio sqrt(9) : sqrt(16) which is 3:4.
Or perimeters are also in the ratio 3:4.
The sum of perimeters is 35.
Or individual perimeters are (3/7)*35 = 15 and (4/7)*35 = 20.

So perimeters are 15 and 20.

Rahul Lakhani
Quant Expert
Gurome, Inc.
https://www.GuroMe.com
On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
1-800-566-4043 (USA)
+91-99201 32411 (India)

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

559 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review