Question

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

• A. Greater
• B. Lesser
• C. Equal
• D. Not sure

Answer 1

The correct option is A

Greater

This property can be verified from the below example –

In the above figure, $\Delta$PQR has
PQ = 4.5 cm
QR = 8 cm
PR = 6 cm
Now if you observe,
PQ + QR > PR
4.5 + 8 > 6
12.5 > 6 (True)

QR + PR > PQ
8 + 6 > 4.5
14 > 4.5 (True)

PR + PQ > QR
6 + 4.5 > 8
10.5 > 8 (True)
Hence, sum of two sides of a triangle is always greater than the third side.