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

10^2 (10 squared) + 15^2 = C^2
100+225=c^2
325=c^2
√325
√25⋅13
√ 25 ⋅√13
5√ 13√325≈18.027756377319946
The whole number would be 5√ 13
It's the converse of the Pythagorean theorem.

Answer 2

The smallest possible whole-number length of the unknown side is
`19\ inches`

Explanation:

we know that

The triangle inequality theorem, states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side

Let

x-----> the length of longest side

Applying the triangle inequality theorem

case A)

`10+15 > x`

`25 > x`

Rewrite

`x< 25`

case B)

`10+x > 15`

`x > 15-10`

`x> 5`

The solution of the third side is the interval------->
`(5,25)`

but remember that

In an obtuse triangle

`x^(2) > a^(2) +b^(2)`

`x^(2) > 15^(2) +10^(2)`

`x > 18.03\ inches`

Round to a whole number

`x= 19\ inches`