(a) We assume the triangle to be a right angle triangle, we can use the Pythagoras theorem to proof whether the third side could be 6 cm. Let say the side of 3cm and 4cm are the two short sides, then
[tex] 3^{2}+ 4^{2}=9+16=25 [/tex]
[tex] \sqrt{25} =5[/tex]
The third side couldn't be 6 for a right angle triangle.
However, if the triangle isn't a right angle, we can construct a scalene triangle of 3cm, 4cm, and 6cm
(b) Similar to part (a), we assume the triangle to be a right-angle triangle, we take the hypotenuse to be 4cm and one shorter side to be 3 cm. Working out the other short side
[tex] 4^{2}- 3^{2} =16-9=7 [/tex]
[tex] \sqrt{7} =2.65[/tex]
In conclusion, we can't have a right angle triangle with sides 4cm, 3cm, and 1 cm
We, however, can construct a scalene triangle of sides 4cm, 3cm and 1 cm
