product of the perpendicular to the square the hypotenuse

Expert replies

bhumika.k.shah: Legendary Member; Posts: 941; Joined: Sun Dec 27, 2009 12:28 amFollowed by: 1 member; Thanked: 20 times

by bhumika.k.shah » Tue Jan 12, 2010 8:46 am

Twice the product of the perpendicular sides of a right-angled triangle is equal to the square of the hypotenuse.Find the perimeter of the triangle if the area is 32 sq.cm

A.16+4sq rt 2cm
B.12+6sq rt 2cm
C.16+8sq rt 2cm
D.10+2sq rt 5cm

OA C

Like this post

Source: Beat The GMAT — Problem Solving | Tue Jan 12, 2010 8:46 am

sunil_snath: Senior | Next Rank: 100 Posts; Posts: 39; Joined: Wed Nov 18, 2009 8:41 am; Thanked: 3 times

by sunil_snath » Tue Jan 12, 2010 9:19 am

Let the sides be 'a' and 'b' and the hypotenuse 'c'.

According to the question:

2(ab) = c^2

Now .5(ab) = 32 (Area). therefore, ab = 64

from the above 2 equation, c = 8sqrt(2)

Now, c^2 = a^2 + b^2
2ab = (a+b)^2 - 2ab
4ab = (a+b)^2
(a+b) = 16

Now a+b = 16 and ab=64, therefore, a = b = 8

perimeter = 16+8sqrt(2)

Is there a faster method of solving this?

Like this post

bhumika.k.shah: Legendary Member; Posts: 941; Joined: Sun Dec 27, 2009 12:28 amFollowed by: 1 member; Thanked: 20 times

by bhumika.k.shah » Tue Jan 12, 2010 10:39 am

could you explain in detail

how did u get .5(ab) = 32 ?

sunil_snath wrote:Let the sides be 'a' and 'b' and the hypotenuse 'c'.

According to the question:

2(ab) = c^2

Now .5(ab) = 32 (Area). therefore, ab = 64

from the above 2 equation, c = 8sqrt(2)

Now, c^2 = a^2 + b^2
2ab = (a+b)^2 - 2ab
4ab = (a+b)^2
(a+b) = 16

Now a+b = 16 and ab=64, therefore, a = b = 8

perimeter = 16+8sqrt(2)

Is there a faster method of solving this?

Like this post

Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pmFollowed by: 614 members; Location: Toronto; Thanked: 1710 times; GMAT Score:800

by Stuart@KaplanGMAT » Tue Jan 12, 2010 12:48 pm

bhumika.k.shah wrote:could you explain in detail

how did u get .5(ab) = 32 ?

Area = 1/2 * base * height

For a right angle triangle, the base and height are simply the non-hypotenuse sides, in this case a and b.

So:

Area = 1/2(a)(b) = .5(ab)

To review the other calculations:

2ab = a^2 + b^2
0 = a^2 - 2ab + b^2

For the GMAT, it's good to train yourself to recognize the two special quadratics, perfect squares and differences of squares. Here we have a classic perfect square, which reduces to:

0 = (a-b)^2

giving us:

a = b

So, a=b and ab = 64; accordingly: a=b=8 (for geometry we can ignore negative solutions).

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

Kaplan Exclusive: The Official Test Day Experience | Ready to Take a Free Practice Test? | Kaplan/Beat the GMAT Member Discount
BTG100 for $100 off a full course

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

560 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