is it possible to form a triangle with given side lengths

Question

we need to figure out if the object is a triangles using the given lengthand if not why not

Answer 1

The cosine rule a^2=b^2+c^2-2bccosA will tell you what the angle is, if it exists, for a=8, b=3, c=4: 64=9+16-24cosA. So cosA=-(64-25)/24=-39/24=-13/8 which is less than -1, so the angle doesn't exist because cosine cannot be bigger than 1 or less than -1. If the angle doesn't exist, then neither does the triangle. You can also see this if you lay the sides 3" and 4" flat to make a line 7" long. 8" is longer than this. The maximum length of the third side must be less than 7". The angle between the shorter sides must be less than 180 degrees.

Answer 2

is it possible to form a triangle with given side lengths

Yes, and no!

Let's say you have been given thrre lengths to use to construct a triangle. Call them l1, l2, l3.

Draw a straight line of length = l1.

Now get a pair of compasses and puting the point at one end of the line l1, draw an arc of radius r = l2.

Now put the point at the other end of the line l1, and draw an arc of radius r = l3.

These two arcs will intersect, but only if l1 < l2 + l3.

If they do intersect, then you have constructed a triangle from 3 given lengths.

Comments

A bit subtle, this one, because the side lengths are given below the text of the question. I guess it's a bit late for trick or treat, but this is definitely a trick!

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Aha! Now I see the side lengths. 3", 4" and 8".

I thought those were just tags, amd so of course just ignored them.

Ib which case the answer to your question is no! Becsause ...

l1 = 8", l2 = 3", l3 = 4" and l1 > l2 + l3