If two sides of a triangle are $3$ $3$ and $5$ $5$ , in what interval can we have the third side?

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Answer 1 · 2017-01-30T04:28:59

Possible values of third side would be in the interval $(2, 8)$ $(2,8)$ , not including $2$ $2$ and $8$ $8$ .

If $3$ $3$ and $5$ $5$ are two sides of a triangle, the third side say $x$ $x$ , will be such that $x < 8$ $x<8$ .

Further, if i is smallest side of triangle, we will have $5 < 3 + x$ $5<3+x$ i.e. $x > 2$ $x>2$

Hence, possible values of third side would be in the interval $(2, 8)$ $(2,8)$ , not including $2$ $2$ and $8$ $8$ .

If two sides of a triangle are 33 and 55, in what interval can we have the third side?