If the perimeter of a triangle is 18, then the length of one of the

Question

If the perimeter of a triangle is 18, then the length of one of the sides CANNOT be

(A) 1 
(B) 3 
(C) 6
(D) 8 
(E) 9

Luckisnoexcuse · Answer

one side should always be less than the sum of other two sides
if one side is 9 then the sum of other two sides will be 9..not possible

E

kunalsinghNS · Answer

We know that sum of any two sides of a triangle is greater than the side

hence if the length of a side is 9 then sum of the other two sides will 9 considering the perimeter as 18
under given condition the above scenario is not possible hence the answer is E

raki99 · Answer

one side should always be less than the sum of other two sides
if one side is 9 then the sum of other two sides will be 9..not possible

E
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hwgmat2015 · Answer

I understand why E is the answer. But why not option A ? if one side is 1, the other two sides will be 8 and 9. These cannot be the sides of the triangle. 
Can someone please explain?

spandey23 · Answer

Yes, why not A?the other two sides can be 10 and 7 as well.

arvind910619 · Answer

it can not be A
let us take the case of an equilateral triangle
perimeter is given to be 18 mm
So each side would be 6 mm
Now we have property of the triangle = a-b<c<a+b
Since each side is equal a-b=0
a+b=12
so 0<c<12 but we know that perimeter is 18 so C<=6
I hope it is clear

rocko911 · Answer

I need help

A) 1 should be greater than SUM OF OTHER 2 SIDES and Less than SUBTRACTION OF 2 SIDES

So if one side is 1 other 2 will be x+y = 17 (well it satisfies that 3rd side should be less than addition of rest 2 so 1 is valid)
But for subtraction? Lets take x= 9 , y =8 , SO 9-8 = 1 , HENCE IT SHOULD BE GREATER THAN 1 to satisfy second condition but its equal to 1 then

IT MEANS 1 CANT BE INCLUDED

PLEASE EXPLAIN

chetan2u · Answer

hi  rocko911  and  hwgmat2015 ..

the Q is looking for CANNOT be, which means it should not be possible..

now you are looking for a triangle with sides 1,8,9 but it can be 8.5,8.5 and 1...
it is nowhere mentioned that sides are INTEGERS

rocko911 · Answer

yes indeed, But its also not mentioned that it cant be integers as well , so we need to take all posibilities,

SO WHAT IF WE TAKE ONE SIDE AS 1 and other two be 9+8 , then it doesnt hold for subtraction rule
becoz 9-8 = 1 and it should be greater than 1

AND IF ITS NOT SATISFYING THEN IT MEANS IT SHOULD "NOT" BE POSSIBLE just as everyone says 9 is

chetan2u · Answer

hi..

CANNOT be means  it is NOT possible under any circumstances

so for any value of other two sides if 1 is possible, then it will not come under CANNOT be.

however 9 is NOT possible under any circumstances so it is our answer

for that matter 3 will not be possible if sides are 3, 7,10..
you will always have value for which each choice will not be possible..

hope it helped

daboo343 · Answer

Here E must be the answer.
as we know the sum of two sides must be greater than the third side. so if one side is 9 so sum of other two side will also be 9 and it violates rules mentioned earlier
Hence E

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If the perimeter of a triangle is 18, then the length of one of the

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