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



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In a certain right triangle, the sum of the lengths of the 01 Nov 2005, 09:09
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sudhagar
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
Show more


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.
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In a certain right triangle, the sum of the lengths of the 01 Nov 2005, 09:11
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Answer : A

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

Taking answer choices, 24^2 + 10^2 = 26^2.
Hence A.
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In a certain right triangle, the sum of the lengths of the 01 Nov 2005, 12:35
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yep, is one of the typical right triangles

13-12-5

so

26-24-10
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In a certain right triangle, the sum of the lengths of the 01 Nov 2005, 12:44
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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...
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sudhagar
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In a certain right triangle, the sum of the lengths of the 01 Nov 2005, 14:12
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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



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Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
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