Question

Please solve q 111 ?

Answer 1

(3) 2

Explanation:

The number of non-congruent triangles with integer sides and perimeter 15 is the same as the number of triplets of positive integers that sum to 15 but where all numbers are less than half of 15. (Each side of a triangle needs to be shorter than the sum of the other two sides.)

The triplets we can get are:

`(7, 7, 1)" "(7, 6, 2)" "(7, 5, 3)" "(7, 4, 4)`
`(6, 6, 3)" "(6, 5, 4)`
`(5, 5, 5)`

There are `m=7` triplets.

Likewise, the triplets for triangles with perimeter 16 are:

`(7, 7, 2)" "(7, 6, 3)" "(7, 5, 4)`
`(6, 6, 4)" "(6, 5, 5)`

There are `n=5` triplets.

The difference is `m-n=2`.