Question

Can a triangle have three sides measuring:

$2cm,3cm,4cm$?

Answer 1

According to the property of a triangle,

Sum of any two sides of a triangle is greater than the third side.

The given sides of the triangle are $2cm,3cm,4cm$.

In $1^{st}$ condition, we will take $2cm\mathrm{and}3\mathrm{cm}$ and add them, the result should be greater than $4cm$.

$2cm+3cm=5cm$ and $5cm>4cm$.

In $2^{nd}$ condition, we will take $3cm\mathrm{and}4\mathrm{cm}$ and add them, the result should be greater than $2cm$.

$3cm+4cm=7cm$ and $7cm>2cm$.

In $3^{rd}$ condition, we will take $2cm\mathrm{and}4\mathrm{cm}$ and add them, the result should be greater than $3cm$.

$2cm+4cm=6cm$ and $6cm>3cm$.

Therefore, It is proved that the sum of any two sides of a triangle is greater than the third side.

Hence, a triangle can have three sides measuring $2cm,3cm,4cm$.