The side length of a non-degenerate - ABC are 4-11 and x- Which of the following is a possible value of x -A- 17B- 7C- 12D- 15

The correct option is C 12Suppose x be the largest side in the triangle, then 4+11 gt; x x lt; 15.——(i) Consider x is the second largest side, then 4+x ...

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Standard IX

Mathematics

Triangle Inequality 2

The side leng...

Question

The side length of a non-degenerate $Δ$ ABC are 4,11 and x. Which of the following is a possible value of x?

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Solution

The correct option is A 12
Suppose x be the largest side in the triangle,
then 4+11 > x $⟹$ x < 15.------(i)

Consider x is the second largest side, then
4+x >11 $⟹$ x > 7 ------(ii)

x cant be the smallest side, because trinagle inequality not get valid in that situation. That is if x < 4 , then x+4 can't be greater than 11.

So from (i) and (ii), the possible value is 12.

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The side length of a non-degenerate Δ ABC are 4,11 and x. Which of the following is a possible value of x?

The side length of a non-degenerate $Δ$ ABC are 4,11 and x. Which of the following is a possible value of x?