Question

the sides of a triangle have lengths 10 cm, 6.5 cm ,x
where X is a whole number. the minimum value that x can take as is ( with reasons)
a) 6
b)5
c)3
d)4​

Answer 1

The minimum value of x is 4 cm.

Step-by-step explanation:

It is given that lengths 10 cm, 6.5 cm, and x cm are the sides of a triangle.

We know that if two sides of a triangle are of lengths a and b, then the third side length c ranges from (a - b) to (a + b), but not including them i.e. (a - b) < c < (a + b).

Now, in our case (10 - 6.5) < x < (10 + 6.5)  

⇒ 3.5 < x < 16.5

So, the minimum value of x is governed by the condition x > 3.5, but it is given that x is a whole number.

Therefore, the minimum value of x is 4 cm. (Answer)

Answer 2

Step-by-step explanation:

The minimum value of x is 4 cm.

Step-by-step explanation:

It is given that lengths 10 cm, 6.5 cm, and x cm are the sides of a triangle.

We know that if two sides of a triangle are of lengths a and b, then the third side length c ranges from (a - b) to (a + b), but not including them i.e. (a - b) < c < (a + b).

Now, in our case (10 - 6.5) < x < (10 + 6.5)  

⇒ 3.5 < x < 16.5

So, the minimum value of x is governed by the condition x > 3.5, but it is given that x is a whole number.

Therefore, the minimum value of x is 4 cm. (Answer)