In a certain right triangle, the sum of the lengths of the

Oldest

Best Reply

Author

Message

TAGS:

Senior Manager

Joined: 02 Oct 2005

Posts: 307

Followers: 1

Kudos [?]: 2 [0], given: 0

In a certain right triangle, the sum of the lengths of the [#permalink]

01 Nov 2005, 08:52

00:00

Question Stats:

0% (00:00) correct

0% (00:00) wrong

based on 1 sessions

In a certain right triangle, the sum of the lengths of the
two legs and the hypotenuse is 60 inches. If the hypotenuse
is 26 inches, which of the following is the length of one of
the legs?

A. 24 inches
B. 34 inches
C. 29 inches
D. 16 inches
E. 13 inches

SVP

Joined: 24 Sep 2005

Posts: 1913

Followers: 6

Kudos [?]: 55 [0], given: 0

Re: PS: Length of Triangle [#permalink]

01 Nov 2005, 09:09

sudhagar wrote:

Let a, b be the two legs and c be the hypotenuse
we have: a+b+c = 60 ----> a+b= 60-26=34 ---> b= 34-a
c^2= a^2+b^2= 26^2= 676
Substitute b into the 2nd equation, we get:
a^2+ (34-a)^2= 676 ....solve this quadratic equation, we get a = 24
A it is.

Director

Joined: 24 Oct 2005

Posts: 666

Location: London

Followers: 1

Kudos [?]: 6 [0], given: 0

[#permalink]

01 Nov 2005, 09:11

Answer : A

hyp = 26. So sum of lengths = 60-26 = 34.

Taking answer choices, 24^2 + 10^2 = 26^2.
Hence A.

Manager

Joined: 20 Mar 2005

Posts: 203

Location: Colombia, South America

Followers: 1

Kudos [?]: 2 [0], given: 0

[#permalink]

01 Nov 2005, 12:35

yep, is one of the typical right triangles

13-12-5

so

26-24-10

Current Student

Joined: 28 Dec 2004

Posts: 3439

Location: New York City

Schools: Wharton'11 HBS'12

Followers: 11

Kudos [?]: 134 [0], given: 2

[#permalink]

01 Nov 2005, 12:44

A it is...

tried a few choices...wasnt getting the right answer, then, picked one of the famous triangles, 3-4-5 that didnt work, 5-12-13...works fine...

Senior Manager

Joined: 02 Oct 2005

Posts: 307

Followers: 1

Kudos [?]: 2 [0], given: 0

[#permalink]

01 Nov 2005, 14:12

Thats correct guys, OA is A

Here is the detailed explanation:
The Pythagorean theorem states that the sum of the squares of the lengths of the legs of a triangle is equal to the square of the length of the hypotenuse.

Let A and B be the lengths of the sides. Let C be the length of the hypotenuse. Thus, we can set up the following equation:

A2 + B2 = C2

We are told that the sum of the legs and hypotenuse is 60 inches. We are also told that the hypotenuse is 26 inches. Thus, we can set up the following equation:

A + B + 26 = 60
A + B = 34
A = 34 - B

Plugging the value of A and C into the first equation:

(34 - B)2 + B2 = 262
(34 - B)(34 - B) + B2 = 676
1156 - 68B + B2 + B2 = 676
2B2 - 68B + 1156 = 676
2B2 - 68B + 480 = 0
(2B - 48)(B - 10) = 0
B = 10 or B = 24

[#permalink] 01 Nov 2005, 14:12

		Similar topics	Author	Replies	Last post
Similar Topics:		In a certain right triangle, the sum of the lengths of the	Geethu	2	31 Mar 2004, 10:35
	1	A certain right triangle has sides of length x, y, and z,	vivektripathi	7	07 Sep 2008, 08:15
	8	A certain right triangle has sides of length x, y, and z	vibhaj	15	17 Jan 2010, 02:39
		Standard lengths of right triangles	nickk	4	28 Feb 2010, 04:33
	9	A certain right triangle has sides of length x, y, and z	tonebeeze	10	16 Jan 2011, 16:01

In a certain right triangle, the sum of the lengths of the

Main navigation

GMAT Resources

Partners

MBA Resources

GMAT ® is a registered trademark of the Graduate Management Admission Council ® (GMAC ®). GMAT Club's website has not been reviewed or endorsed by GMAC.

GMAT Courses

Admissions Consulting

In a certain right triangle, the sum of the lengths of the

In a certain right triangle, the sum of the lengths of the

Main navigation

GMAT Resources

Partners

MBA Resources