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?

24 inches.

Step-by-step explanation:

Two sides of an obtuse triangle measure 10 inches and 15 inches.

The length of the longest side is unknown.

We have to find the smallest possible whole number for length of the unknown side.

Since a triangle is possible only when sum of two sides of the triangle is greater than the third side.

Therefore, length of third side < sum of other two sides

length of third side < 10 + 15

length of third side < 25

Therefore smallest whole number length should be 24 inches.

A^2 + b^2 = c^2

10^2 = 100

15^2 = 225

100+225 = 325

square root of 325 is approximately 18

Unknown side is about 18 inches