Question

Chang knows one side of a triangle is 13 cm. Which set of two sides is possible for the lengths of the other two sides of this triangle?

Answer 1

The sum of the other 2 sides must be greater than 13.

Answer 2

Possible lengths of other two sides can be 5 and 12.

Explanation:

Let the given triangle be a scalene triangle.

Then, the condition for three sides to form a triangle is sum of any two sides should be greater than the third side.

Take 5 and 12.

Now, 5 + 12 = 17 > 13

12 + 13 = 25 > 5

13 + 5 = 18 > 12

Hence, 5, 12 and 13 are possible lengths of sides of a triangle.

Moreover, if the given triangle is right angled, and its hypotenuse is 13,

then, by Pythogoras theorem,

`13^(2) =5^(2) +12^(2)`

Hence, the possible lengths of other two sides can be 5 and 12.