Question

The sides of a triangle have lengths(in cm) 10, 6.5 and a, where a is a whole number. Find the minimum and maximum value of 'a', which it can take.
[4 marks]

Answer 1

We know, the sum of any two sides in a triangle is always greater than the third side.
(0.5 mark)

So, 10 + 6.5 > a
16.5 > a
(0.5 mark)

'a' is a whole number and it's less than 16.5. So, its maximum value will be 16.
(1 mark)

For the minimumm value of 'a' , we will use the fact that the difference of two sides is always less than the third side
(0.5 marks)

So, 10 - 6.5 < a
3.5 < a
(0.5 marks)

'a' is a whole number and it's greater than 3.5. So, its minimum value will be 4.
(1 mark)