Question

The sides of a triangle are of length 8 cm and 4 cm the length of the third side of the triangle cannot be {4.1},{5.3},{3.9},{4.5}

Answer 1

${\bold{\underline{\underline{Answer:}}}}$

${\bold{\therefore Not\:Possible\:side=3.9\:cm}}$

${\bold{\therefore Possible\:third\:side=4.1\:cm,5.3\:cm,4.5\:cm}}$

${\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\underline \bold{Given : } \\ \implies First\: side = 8 \: cm \\ \\ \implies Second \: side = 4 \: cm \\ \\ \underline \bold{To \: Find: } \\ \implies Third \: side \: cannot \: be \: possible = ?$

• According to given question :

$\bold{Using \: triangle \: property} \\ \implies Sum \: of \: two \: sides \: is \: always \: greater\\ \: \: \: \: \: \: \: \: \: \: than \: or \:equal \: to \: third \: side \\ \\ \bold{Taking \: third \: side = 4.1 \: cm} \\ \implies Second \: side+ Third \: side \geqslant Largest \: side \\ \\ \implies 4 + 4.1 \geqslant 8 \\ \\ \implies 8.1 \geqslant 8 \\ \\ \bold{Taking \: third \: side = 5.3 \: cm} \\ \implies Second \: side+ Third \: side \geqslant Largest \: side \\ \\ \implies 4 +5.3 \geqslant 8 \\ \\ \implies 9.3 \geqslant 8 \\ \\ \bold{Taking \: third \: side = 3.9\: cm} \\ \implies Second \: side+ Third \: side \geqslant Largest \: side \\ \\ \implies 4 +3.9 {\geqslant} 8 \\ \\ \implies 7.9 \cancel{\geqslant }8 \\ \\ \bold{Taking \: third \: side = 4.5 \: cm} \\ \implies Second \: side+ Third \: side \geqslant Largest \: side \\ \\ \implies 4 + 4.5 \geqslant 8 \\ \\ \implies 8.5 \geqslant 8 \\ \\ \bold{So, \: from \: these \: four \: conclusion \: comes \: that \: 3.9\:cm } \\ \bold{can't \: be \: possible \: as \: third \: side}$

Answer 2

$\bold{using \: triangle \: property} \\ \implies sum \: of \: two \: sides \: is \: always \: greater\\ \: \: \: \: \: \: \: \: \: \: than \: or \:equal \: to \: third \: side \\ \\ \bold{taking \: third \: side = 4.1 \: cm} \\ \implies second \: side+ third \: side \geqslant largest \: side \\ \\ \implies 4 + 4.1 \geqslant 8 \\ \\ \implies 8.1 \geqslant 8 \\ \\ \bold{taking \: third \: side = 5.3 \: cm} \\ \implies second \: side+ third \: side \geqslant largest \: side \\ \\ \implies 4 +5.3 \geqslant 8 \\ \\ \implies 9.3 \geqslant 8 \\ \\ \bold{taking \: third \: side = 3.9\: cm} \\ \implies second \: side+ third \: side \geqslant largest \: side \\ \\ \implies 4 +3.9 {\geqslant} 8 \\ \\ \implies 7.9 \cancel{\geqslant }8$