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What is the perimeter of a certain right triangle?

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What is the perimeter of a certain right triangle? [#permalink]

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New post 06 Mar 2017, 01:13
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What is the perimeter of a certain right triangle?

1) The hypotenuse’s length is 10
2) The triangle’s area is 24
[Reveal] Spoiler: OA

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Re: What is the perimeter of a certain right triangle? [#permalink]

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New post 06 Mar 2017, 03:52
prompt analysis
let the other two sides be a and b. hypotenuse = (a^2 +b^2 )^1/2
area = ab/2

superset
the answer will be a positive real number.

Translation
In order to find the answer, we need:
1# exact value of a and b
2# two equation in a and b
3# the value of the product ab

statement analysis
St 1: (a^2 +b^2 )^1/2 = 10. two variable, one equation. INSUFFICIENT
St 2: ab/2 = 24. two variable, one equation. INSUFFICIENT.

St 1 & St 2: two variable, two equation. Can be calculated. SUFFICIENT.

Option C

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Re: What is the perimeter of a certain right triangle? [#permalink]

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New post 06 Mar 2017, 04:21
Because we know 10 is the hypotenuse so it should be from the set (6,8,10). Option 1 sufficient
Area is 24. Ie base * height = 24 * 2 = 48
48 we factorize and see if any of the no:S from right triangle set is derived i.e.
48= 2^4 * 3, which is 8*6 and 12* 4. 4,12 doesn't form a set of right triangle sides but 6,8 forms a set and the third side is 10. Therefore perimeter is 24 .
Thus option D.


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Re: What is the perimeter of a certain right triangle? [#permalink]

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New post 08 Mar 2017, 01:12
==> In the original condition, for a right triangle, there are 2 variables (2 legs) and in order to match the number of variables to the number of equations, there must be 2 equations. Since there is 1 for con 1) and 1 for con 2), C is most likely to be the answer. By solving con 1) and con 2), you get 6:8:10 and the perimeter of the right triangle becomes 6+8+10=24, hence unique and sufficient.

Therefore, the answer is C.
Answer: C
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Re: What is the perimeter of a certain right triangle? [#permalink]

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Question : Can you please elaborate more the answer? How did you get the 6 and 8?

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Re: What is the perimeter of a certain right triangle? [#permalink]

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New post 06 Sep 2017, 22:44
MathRevolution wrote:
What is the perimeter of a certain right triangle?

1) The hypotenuse’s length is 10
2) The triangle’s area is 24


The trick with this question is that in statement 1 we cannot actually assume that the sides are 6 and 8 just because we know that

x^2 +y^2 = 100

We cannot make any assumptions about X and Y UNLESS there is a restriction such as "X and Y must be integers" or "The product of XY is 48."

C

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Re: What is the perimeter of a certain right triangle? [#permalink]

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New post 09 Sep 2017, 21:29
arpanmagoo wrote:
Question : Can you please elaborate more the answer? How did you get the 6 and 8?


Assume we have two sides \(a\) and \(b\) and a hypothesis 10.
Then we have \(a^2 + b^2 = 100\) and \(\frac{1}{2}ab = 24\)
Thus \(a = 6\), \(b = 8\) or \(a = 8\), \(b = 6\).
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Re: What is the perimeter of a certain right triangle?   [#permalink] 09 Sep 2017, 21:29
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