Question

Which set of measurement could be the side lengths of a triangle. Select all that apply.A. 3cm, 3cm, 3cmB. 4cm, 8cm, 12cmC. 5cm, 9cm, 14cmD. 6cm, 7cm, 8cmE. 7cm, 7cm, 10cm

Answer 1

To solve the question, we will apply the principle

If the sides are not equal, the sum of the two shortest sides must be greater than the longest sides

For option A

3 cm, 3cm, 3cm

All sides are equal so it satisfies the condition for a triangle

For option B

The sum of the two shorter sides (4cm and 8cm) = 12cm

while the longest side is 12cm

Since the sum of 12cm is not more than the longest side, then

the sides are NOT suitable for a triangle

For option C

5cm + 9cm = 14 cm

The longest side = 14cm

Since the sum 14cm is not greater than the longest side, then

the sides are NOT suitable for a triangle

For option D

Sum of the shorter sides = 6cm + 7cm = 13cm

longest side = 8cm

Since the sum of 13cm is greater than 8cm, then it is suitable for a triangle

For option E

Sum of shorter sides = 7cm + 7cm = 14cm

longer side = 10cm

Since the sum of 14cm is greater than 10cm, then it is suitable for a triangle