Question

If PQ = 25 cm and QR = 8 cm, then what are the possible lengths for PR so that PQ,QR , and PR can form a triangle? Explain your reasoning.

Answer 1

We have been given that length of PQ and QR is 25 cm and 8 cm respectively.

We can find possible side length of PR in order to form a triangle using triangle inequality theorem.

Triangle inequality theorem states that the sum of lengths of two sides of a triangle must be greater than length of third side of triangle.

The length of PR should be either less than sum of PQ and QR or greater than difference of PQ and QR.

`PR<25+8`

`PR<33`

Let us find the other possible length of PR.

`PR>25-8`

`PR>17`

Therefore, the length of PR should be either less than 33 or greater than 17 so that PQ, QR and PR can form a triangle.