Question

2. Sandy made a reflective sticker for her bicycle in the shape of a triangle. Two of the three side lengths were 3 cm and 4 cm.

(a) Could the third side of the reflective sticker be 6 cm long? Explain your reasoning. If this third side is possible, draw the triangle.
(b) Could the third side of the reflective sticker be 1 cm long? Explain your reasoning. If this third side is possible, draw the triangle.

Answer 1

(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

`3^(2)+ 4^(2)=9+16=25`

`√(25) =5`
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

`4^(2)- 3^(2) =16-9=7`

`√(7) =2.65`
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