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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

2 Answers

4 votes

Answer:

I did the test and thecorrect option was 18.

User Kamran Jabbar
by
8.0k points
3 votes

Answer:

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.

User PaPu
by
8.1k points

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