Question

The length of two sides of triangle are $6$cm and $10$cm. Between what two wholes numbers should lie the measure of the third sides?

Answer 1

two sides of triangle are $6,10$

(case 1) :-

let the third side be the smallest side

$x\le 6$

$x+6>10$

$x>4$

$\therefore 4<x\le 6$

$x\in (4,6]$

(case 2) :-

third side be largest

$x⩾10$

$10+6>x$

$x<16$

$x\in [10,16)$

$\therefore$

$x\in (4,16)$

$\therefore$ x should lie in betweenn$4$ and $16$.

and not equal to $4$ and $16$.