BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

product of the perpendicular to the square the hypotenuse

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Problem Solving |
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?
Top
Legendary Member
Posts: 941
Joined: Sun Dec 27, 2009 12:28 am
Thanked: 20 times
Followed by:1 members

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?
Top
User avatar
GMAT Instructor
Posts: 3225
Joined: Tue Jan 08, 2008 2:40 pm
Location: Toronto
Thanked: 1710 times
Followed by:614 members
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).
Image

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
Top
Post new topic Post Reply
• Page 1 of 1