Question

How many different triangles have the perimeter 15 cm if lengths are natural
numbers?​

Answer 1

Answer:

any triangle can have perimeter 15 cm, let the lengths be natural number

Answer 2

Answer:

Let the sides of the triangle be x , y and 12−(x+y) .

Now, the sum of any two sides of a triangle is greater than its third side. So,

x+y>12−(x+y)

∴x+y>6

Also, the difference of the two sides should be less than the third. So,

x−y<12−(x+y)

∴x<6

Since x and y are arbitrary, y<6

Based on the above equations, x and y lies between 1 and 5. The acceptable unique pairs of x and y are:

(2, 5)

(3, 4)

(3, 5)

(4, 4)

(4, 5)

(5, 5)

While calculating the third side, we can see that pairs 1 and 6, and 2, 3 and 5, are the same. So we have 3 triangles:

(2, 5, 5)

(3, 4, 5)

(4, 4, 4)