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# What is the perimeter of a certain right triangle?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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What is the perimeter of a certain right triangle?  [#permalink]

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06 Mar 2017, 01:13
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Difficulty:

45% (medium)

Question Stats:

60% (01:31) correct 40% (01:17) wrong based on 106 sessions

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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

_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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"Only $149 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Director Status: Come! Fall in Love with Learning! Joined: 05 Jan 2017 Posts: 542 Location: India Re: What is the perimeter of a certain right triangle? [#permalink] ### Show Tags 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 _________________ GMAT Mentors Intern Joined: 09 Nov 2016 Posts: 36 Re: What is the perimeter of a certain right triangle? [#permalink] ### Show Tags 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. Sent from my iPhone using GMAT Club Forum Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 7224 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: What is the perimeter of a certain right triangle? [#permalink] ### Show Tags 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 _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$149 for 3 month Online Course"
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Re: What is the perimeter of a certain right triangle?  [#permalink]

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13 Mar 2017, 06:05
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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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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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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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