The numerical value of the product of the sides of atriangle is 512 un

1.	The numerical value of the product of the sides of atriangle is 512 units. Find the minimum possibleperimeter of the triangle (in units).
Answer» Step-by-step EXPLANATION: We KNOW that the SUM of any TWO sides of a triangle is greater than the third side. ....(1) Here the perimeter of the triangle is 14 units. Let divide 14 into 3 parts, so that a+b+c=14, when a,b and c are integers. To COMPLY with (1), the sum of any two of a,b or c should be greater than 2 14 =7. Such possible combinations are (i) 2+6+6 (ii) 3+5+6 (iii) 4+5+5 (iv) 4+6+4 No other combination is possible. So, number of distinct triangles are 4.

The numerical value of the product of the sides of atriangle is 512 units. Find the minimum possibleperimeter of the triangle (in units).

Answer»

Step-by-step EXPLANATION:

We KNOW that the SUM of any TWO sides of a triangle is greater than the third side. ....(1)

Here the perimeter of the triangle is 14 units.

Let divide 14 into 3 parts, so that a+b+c=14, when a,b and c are integers.

To COMPLY with (1), the sum of any two of a,b or c should be greater than

=7.

Such possible combinations are

(i) 2+6+6

(ii) 3+5+6

(iii) 4+5+5

(iv) 4+6+4

No other combination is possible.

So, number of distinct triangles are 4.