Question

If two sides of a triangle have lengths 4 and 9, then the length of the third side may be any numberA. greater than 5B. greater than 4 but less than 9C. less than 13D. greater than 5 but less than 13

Answer 1

The triangle is possible if sum of length of any two sides of triangle is more than third side.

In given triangle length of sides of triangle are 4 and 9.

Determine the sum of two sides of triangle.

`4+9=13`

The sum of two sides of triangle is 13, which means the third side of triangle must be less than 13 as triangle is possible if sum of two sides of triangle is more than third side.

Since it is known that third side of triangle is less than 13 but if we take third side be 5 then sum of side 4 and side 5 is 9 which is equal to side of triangle with length 9. This means that third side must be greater than 5 but less than 13.

So answer is greater than 5 but less than 13.