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? 18 inches 19 inches 24 inches 25 inches

Answer 1

I did the test and thecorrect option was 18.

Answer 2

19 inches is the correct answer.

Explanation:

Side 1 = 10 inches

Side 2 = 15 inches

It is given that it is an obtuse angle triangle i.e. the largest angle of the triangle is more than
`90^\circ`.

Let us suppose, that the triangle be a right angle triangle, then the largest angle will be
`90^\circ`. The largest side is known as Hypotenuse.

As per pythagoras theorem:

`Hypotenuse^(2) = Base^(2) + Height^(2)`

`\Rightarrow 10^(2) + 15^(2) = Hypotenuse^2\\\Rightarrow 325 = Hypotenuse^2\\\Rightarrow Hypotenuse = 18.04\ inches`

So, largest side comes out be 18.04 inches.

But actually, the largest angle is more than
`90^\circ` so the largest side will also be greater than 18.04 inches.

Hence, the answer is:

Smallest possible whole number length of unknown side will be 19 inches.