So we are given the measurements of two sides of a Triangle:
(write down the given to be clear)
PQ=21 cm
QR=5 cm
But one very important thing:
As Aman said, the length of PR would definitely not be greater than the sum of the other two sides/legs....
Why? Because then it gives a STRAIGHT LINE!
which means: PR will be less than that sum
PR<sum of PQ and QR
PR<21+5
PR<26
Time for Pythagoras Theorem!
We can now split it into Two ways, since we dont know if PR is just a leg or the hypotenuse of the triangle:
And therefore:
Assuming PR is a leg:
(PQ seems to be the larger number)
PQ²=PR²+QR²
21² =PR²+5²
21²-5²=PR²
√21²-5²=PR
20.396 cm=PR
≈20.4 cm
20.4≤PR<26 (which means it can be 20.4 as well, but not any lower as it is very obvious)
Assuming that PR is the hypotenuse:
PR²=PQ²+QR²
PR²=21²+5²
PR=√21²+5²
PR=21.587 cm≈ 21.6 cm
21.6≤PR<26
So basically, the length can be 21.6 itself or higher.