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11 Jul 2016, 18:31
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
68% (01:23) correct
32%
(01:33)
wrong
based on 136
sessions
History
Date
Time
Result
Not Attempted Yet
What is the perimeter of a certain right triangle?
1) The hypotenuse’s length is 5
2) The triangle’s area is 4.5
*An answer will be posted in 2 days.
1) The hypotenuse’s length is 5
2) The triangle’s area is 4.5
*An answer will be posted in 2 days.
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
Data Sufficiency Forum
11 Jul 2016, 21:40
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Statement 1: insufficient
we don't have any information about the other sides. If other sides are 3,4 then the area is different from area in the case where other sides are both sqrt(25/2).
Statement 2: insufficient
1/2*(product of other sides) = area
So, Knowing the area of the triangle won't be enough to know the length of all sides.
Statement 1+2: sufficient
let other sides be a and b.
we know that 1/2*(a*b) = 4.5 and (a^2+b^2)=5^2.
Solving the above, we will get a^2=9 or 16. So, either a=3 and b=4 or a=4 and b=3.
Perimeter = 3+4+5 = 12 in both cases.
Hence, sufficient and answer will be C.
-----------------------------------------------------
P.S. Don't forget to give kudos
we don't have any information about the other sides. If other sides are 3,4 then the area is different from area in the case where other sides are both sqrt(25/2).
Statement 2: insufficient
1/2*(product of other sides) = area
So, Knowing the area of the triangle won't be enough to know the length of all sides.
Statement 1+2: sufficient
let other sides be a and b.
we know that 1/2*(a*b) = 4.5 and (a^2+b^2)=5^2.
Solving the above, we will get a^2=9 or 16. So, either a=3 and b=4 or a=4 and b=3.
Perimeter = 3+4+5 = 12 in both cases.
Hence, sufficient and answer will be C.
-----------------------------------------------------
P.S. Don't forget to give kudos
12 Jul 2016, 10:12
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MathRevolution
-------------------------
A rather easier method :
Consider the other two sides of the traingle as a,b
1) Shows that that hypotenuse is 5 , hence a^2 + b^2 = 25
So here we can't find the perimeter by just this information
2) Shows that Area = 4.5 , or (1/2 *a*b)= 4.5 , or ab=9
So here we can't find the perimeter by just this information
Now combining both
(a+b) ^2 = a^2+b^2 + 2*a*b = 25+18=43, or a+b = √43
Hence perimeter = a+b+5 = √43+5
Hence C.
