A triangle has side lengths of 16cm, 63cm, and 65cm. Classify it as acute, obtuse or right. Please hel!!!

9514 1404 393

  right

Step-by-step explanation:

If you're going to be in the business of classifying triangles based on side lengths, it can be useful to know there is a "form factor" that can help. For sides a, b, c, with long side 'c', it is computed as ...

  f = a² + b² - c²

It has the following interpretation with respect to triangle shape:

  f > 0 . . . acute

  f = 0 . . . right

  f < 0 . . . obtuse

__

In this case, we have ...

  16² +63² -65² = 256 +3969 -4225 = 0

The triangle is a right triangle.

Additional comment

When the triangle is a right triangle, this is equivalent to a statement of the Pythagorean theorem: c² = a² + b².

For triangles of other shapes, the interpretation is consistent with the Law of Cosines. When the form factor is divided by 2ab, the result is the cosine of the largest angle. That is why >0 means acute and <0 means obtuse.

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet