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In the right triangle above, a < b. What is a?

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Bunuel
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In the right triangle above, a < b. What is a? [#permalink] New post   06 Jun 2017, 10:14
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A
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E

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58% (01:33) correct 42% (01:34) wrong based on 206 sessions
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In the right triangle above, a < b. What is a?

(1) c = 5

(2) The area of the triangle is 6.

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C
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nishantt7
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Re: In the right triangle above, a < b. What is a? [#permalink] New post   06 Jun 2017, 10:37
Bunuel wrote:

In the right triangle above, a < b. What is a?

(1) c = 5

(2) The area of the triangle is 6.

Show Spoiler
Attachment:
RightTriangle.png



I think the answer should be A.
Statement 1 is sufficient becoz c=5 gives a=3 and b=4. The only possible solution.
Statement 2 gives a=3 and b=4 or a=2 and b=6.
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In the right triangle above, a < b. What is a? [#permalink] New post   Updated on: 06 Jun 2017, 10:51
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Bunuel wrote:

In the right triangle above, a < b. What is a?

(1) c = 5

(2) The area of the triangle is 6.

Show Spoiler
Attachment:
RightTriangle.png




Testing 1st statement:

even if were given that c = 5, it does not necessarily mean that the triangle is of the form 3:4:5, since there could be more options:
Pythagorean theorem ---> \(a^2+b^2=c^2\)
\(1:\sqrt{24}:5\) ------> \(1^2+\sqrt{24}^2 = 25\) Hence, not sufficient

Testing 2nd statement:

\(Triangle Area = \frac{a*b}{2}\), so:
\(\frac{a*b}{2} = 6\) --- > multiplying by 2
\(a*b = 12\)
still,not sufficient

1st+2nd statement combined:

Factors of 12:
1:12
2:6
3:4

only combination that fits with the Pythagorean theorem is 3:4:5

Hence, Answer is (C)

Originally posted by naorba on 06 Jun 2017, 10:50.
Last edited by naorba on 06 Jun 2017, 10:51, edited 1 time in total.
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Re: In the right triangle above, a < b. What is a? [#permalink] New post   06 Jun 2017, 10:51
nishantt7 wrote:
Bunuel wrote:

In the right triangle above, a < b. What is a?

(1) c = 5

(2) The area of the triangle is 6.

Show Spoiler
Attachment:
RightTriangle.png



I think the answer should be A.
Statement 1 is sufficient becoz c=5 gives a=3 and b=4. The only possible solution.
Statement 2 gives a=3 and b=4 or a=2 and b=6.


for St 1 what if a = root(5) and b = 2root(5) (since nothing is said about a or b) this will also satisfy a<b and the Pythagoras theorem.
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Re: In the right triangle above, a < b. What is a? [#permalink] New post   06 Jun 2017, 11:18
It does not say that the sides are integers, therefore we can not find a unique value knowing the hypotenuse and the area. I'd go with E
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In the right triangle above, a < b. What is a? [#permalink] New post   06 Jun 2017, 11:54
alexjst wrote:
It does not say that the sides are integers, therefore we can not find a unique value knowing the hypotenuse and the area. I'd go with E


In order to say that C in not true you need to show that there is at list one more option for values that can fit the 2 statements above: area = 12, and c=5
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In the right triangle above, a < b. What is a? [#permalink] New post   06 Jun 2017, 16:01
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Bunuel wrote:

In the right triangle above, a < b. What is a?

(1) c = 5

(2) The area of the triangle is 6.

Show Spoiler
Attachment:
RightTriangle.png



Fact 1: c =5

No info about b.

Insufficient

(2) The area of the triangle is 6.

1/2 ab =6.......ab =12......No certain info about b.

Insufficient

Combine 1 & 2

For right triangle rule: \(c^{2}\) = \(a^{2}\) + \(b^{2}\)

Multiply the equation in \(b^{2}\)

25\(b^{2}\)= \(a^{2}\)\(b^{2}\) + \(b^{4}\)................Equation A

From fact 2: ab = 12......\((ab)^{2}\)= 144........Substitute in equation A

25\(b^{2}\)= 144 + \(b^{4}\)

\(b^{4}\)- 25\(b^{2}\) + 144 = 0

(\(b^{2}\) - 9) (\(b^{2}\) -16) = 0

\(b^{2}\) = 9 or \(b^{2}\)= 16

Case 1:
b = 3
a =4
Rejected as a < b

Case 2:

b = 4
a =3

Accepted as as a < b

One solution obtained

Answer: C
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In the right triangle above, a < b. What is a? [#permalink] New post   12 Jun 2017, 12:48
Bunuel wrote:

In the right triangle above, a < b. What is a?

(1) c = 5

(2) The area of the triangle is 6.

Show Spoiler
Attachment:
RightTriangle.png


S1 -> Insufficient.
a<b<5 => A and B can take any values that satisfies the pythagorean theorem.

S2 -> Insufficient.
(ab)/2 = 6 => ab = 12
Multiple possible values.

S1+ S2 -> Sufficient
a<b<c
and ab = 12
=> a is 3, b is 4.

The answer is C.
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Re: In the right triangle above, a < b. What is a? [#permalink] New post   30 Dec 2021, 10:38
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Re: In the right triangle above, a < b. What is a? [#permalink]
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