Is the perimeter of a triangle greater than 1?
1). Two of the heights are less than 1/3
2). One of the heights is greater than ½
OA - B
Triangle - perimeter
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1). Two of the heights are less than 1/3
In this case the sides that act as hypotenuse to these heights may also very samll ie less that 1/3, so the perimeter might be or might not be greater that 1
INSUFF
2). One of the heights is greater than ½
Now if we visualise this height in a triangle which is not right angle then
this height will divide the triangle into 2 triangles each of whose hypotenuse is the side of the original triangle hence we can say that two sides itself are greater than 1
SUFF
C
In this case the sides that act as hypotenuse to these heights may also very samll ie less that 1/3, so the perimeter might be or might not be greater that 1
INSUFF
2). One of the heights is greater than ½
Now if we visualise this height in a triangle which is not right angle then
this height will divide the triangle into 2 triangles each of whose hypotenuse is the side of the original triangle hence we can say that two sides itself are greater than 1
SUFF
C
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Samir
Samir
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I think it is B.
I've tried to explain it with reference to (w.r.t) attached doc for different possibilities of triangles.
wr.t attached doc figire 1, two of the heights are less than 1/3, in that case side a can be 1/3 but there is no restirction on the size of b (it can be more than 1 also). So perimiter can be > 1.
wr.t attached doc figure 2, two of the heights are less than 1/3, in that case side a, b & c can be 1/3 . So perimiter can be < 1.
Hence INSUFF.
wr.t attached doc figure 2, side b will be greater than 1/2. Minimum length of a can be 1/2 when it is height itself. Hence the perimiter will be greater than 1.
SUFF.
I've tried to explain it with reference to (w.r.t) attached doc for different possibilities of triangles.
1). Two of the heights are less than 1/3
wr.t attached doc figire 1, two of the heights are less than 1/3, in that case side a can be 1/3 but there is no restirction on the size of b (it can be more than 1 also). So perimiter can be > 1.
wr.t attached doc figure 2, two of the heights are less than 1/3, in that case side a, b & c can be 1/3 . So perimiter can be < 1.
Hence INSUFF.
2). One of the heights is greater than ½
wr.t attached doc figure 2, side b will be greater than 1/2. Minimum length of a can be 1/2 when it is height itself. Hence the perimiter will be greater than 1.
SUFF.
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stmt 1 - two sides are less than 1/3...let's say .32...now third side can be .32 itself making the premieter < 1 or can be 0.5 making perimeter > 1....so insuff
stmt 2 - one side > 0.5..let's say 0.51...now the sum of the other two sides has to be atleast 0.52...so the perimeter will defenitely be > 1...Suff
So ans is B...
stmt 2 - one side > 0.5..let's say 0.51...now the sum of the other two sides has to be atleast 0.52...so the perimeter will defenitely be > 1...Suff
So ans is B...
Trying hard!!!
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Sorry for the confusion the answer is B only, I solved it to show B is sufficient but by mistake wrote C instead of B
Regards
Samir
Samir