A triangle has side lengths of 10,24, and 34. how do i find out what type of triangle it is?

### 7 Answers

Check the value of the longest side squared as compared to the sum of the other legs squared.

If the longest side squared equals the sum of the legs squared, the triangle is a right triangle.

If the longest side squared is less than the sum of the legs squared, the triangle is acute.

If the longest side squared is greater than the sum of the legs squared, the triange is obtuse.

34^2 = 1156

10^2 + 24^2 = 676.

Therefore, the triangle is obtuse.

The two smaller sides are a = 10, and b = 24. The longer side is c = 34. Using pythagora’s theorem: a^2 + b^2 = c^2, we can see what kind of triangle it is. If the values satisfy the equation, it is right angled. If subbing in values for a and b yield a value for c larger than the one given, it is an acute triangle. And if it yields a value of c smaller than the one given, it is an obtuse triangle.

a^2 + b^2 = c^2

10^2 + 24^2 = c^2

100 + 576 = c^2

676 = c^2

c = 26

So we don’t get the right value for c, so it is not a right angled triangle. Since the value of c given is 34, while the one we calculated is 26, it must be an obtuse triangle.

Just as an extra bit of information, this “triangle is actually a line. Considering it has to be a closed space, if you connect the 10 and 24 side lengths together end to end, the other side (34) would reach all the way back to the starting point of the other two lines. So, although it is a “close space” with 3 sides, it isn’t actually a triangle, because it has no area, because the lines completely overlap. But that is besides the point. They wanted to know what kind of triangle it was, so it is obtuse.

Classify Triangles By Sides

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RE:

Classify triangle as acute, right or obtuse?

A triangle has side lengths of 10,24, and 34. how do i find out what type of triangle it is?

Cut out paper strips of those lengths and form the triangle is one way. (I’m guessing obtuse from this visula imagining method)

Someone else can help you with a mathematical way. A right triangle would result if a^2+b^2=c^2 and that does not seem true.

(I think Evelyn is on to something!)

I think you’ll find that since two of the sides sum to make the third side, what you’ve actually got is a straight line and not a triangle. Sorry :o(

a Triangle can’t have lengths 10,24,34 or else the 3 sides will be coinciding as 10+24=34 !!