Question

what is the number of acute angled triangles whose sides are consecutive even numbers and perimeter is less than or equal to 60 cm ?​

Answer 1

Step-by-step explanation:

Assume the sides to be n, n+1, n+2 we have,

Sum of the smallest two sides should be greater than the third side. So

n + (n + 1) > n +2

Or, n > 1

The other condition specified is the perimeter

n+ n + 1 + n+ 2 <= 100

We get 3n <= 97 or n <= 32

So you can list out the combinations

2, 3, 4

3, 4, 5

…..

31, 32, 33

32, 33, 34

If you count you actually have 31 combinations.