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

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Senior Manager
Joined: 02 Oct 2005
Posts: 297
In a certain right triangle, the sum of the lengths of the  [#permalink]

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01 Nov 2005, 08:52
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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: 1885
Re: PS: Length of Triangle [#permalink]

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01 Nov 2005, 09:09
sudhagar wrote:
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

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: 659
Location: London

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01 Nov 2005, 09:11

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: 201
Location: Colombia, South America

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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: 3357
Location: New York City
Schools: Wharton'11 HBS'12

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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: 297

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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
01 Nov 2005, 14:12
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