Question

Two sides of an obtuse triangle measure 10 inches and 15 inches. The length of longest side is unknown. What is the smallest possible whole-number length of the unknown side?

Answer 1

Now one of the most important rule for any triangle to exist is that the sum of two sides should be less than the third

Meaning to say is that

If x, y and z are the lengths of the three sides of the triangle then

x+y ∠ z (z= x+y)

So if you were to obtain the largest side obtain z and substract it by 1

And to find the length of the smallest possible 3rd side when the angle is obtuse is that,

The length of the third side should be just greater than the side which is at hypotenuse

Now, consider that a right angled triangle is formed,

So, the length of the third side

=√(15² + 10²)

=√(225 + 100)

=√325

=18.027

So,

As it is mentioned that the triangle is obtuse

So,

We take the next greater whole number which is

19

So,

The smallest length possible will be 19