Question

Two sides of an obtuse triangle measure 10 inches and 15 inches. The length of longest side is unknown.

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

Answer:

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

Step-by-step 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

$x= 19\ inches$