Question

Verify if the following are the sides of a triangle. Give reason for your answer.

(i) AB = 5.5cm, BC = 4cm, AC = 8 cm
(ii) PQ = 4.5cm, QR = 6.5cm PR = 8cm

Answer 1

To verify if the given sides form a triangle, we need to check if the sum of the two shorter sides is greater than the longest side. The sides (i) AB = 5.5cm, BC = 4cm, AC = 8cm do not form a triangle because the sum of the two shorter sides is not greater than the longest side. The sides (ii) PQ = 4.5cm, QR = 6.5cm, PR = 8cm do form a triangle because the sum of the two shorter sides is greater than the longest side.

Step-by-step explanation:

To verify if the given sides form a triangle, we need to check if the sum of the two shorter sides is greater than the longest side. Let's examine the given sides:

AB = 5.5cm, BC = 4cm, AC = 8cm

Sum of the two shorter sides: AB + BC = 5.5cm + 4cm = 9.5cm

The longest side: AC = 8cm

Since the sum of the two shorter sides is not greater than the longest side, these sides do not form a triangle.

PQ = 4.5cm, QR = 6.5cm, PR = 8cm

Sum of the two shorter sides: PQ + QR = 4.5cm + 6.5cm = 11cm

The longest side: PR = 8cm

Since the sum of the two shorter sides is greater than the longest side, these sides do form a triangle.