Question

2.The sides of triangle have lengths ( in cm) 10, 6.5 and a,
where a is a whole number. What will be the minimum value of
a?

Answer 1

Given:

Three sides of a triangle are 10 cm, 6.5 cm and a cm..

To find:

Minimum value of a.

Solution:

Side lengths of a triangle are 10 cm, 6.5 cm and a cm.

By triangle inequality theorem,

Sum of the lengths of two sides of a triangle is greater than the length of third side.

1). 10 + 6.5 > a

   16.5 > a

   a < 16.5

2). 10 + a > 6.5

    a > -3.5

3). 6.5 + a > 10

    a > 10 - 6.5

    a > 3.5  

Since, measure of a can't be negative or zero.

Therefore, a = 4 cm will be the minimum value of a.