Given the side lengths of 20,23 and 41, determine whether the triangle is acute, right, obtuse, or not a triangle.

Explanation:

In this case, a triangle is possible since adding any two sides leads to a sum larger than the third side

I'm using the triangle inequality theorem here.

To determine what kind of triangle we have, we'll use the converse of the Pythagorean theorem. Specifically, we'll use a corollary of it.

Consider a triangle with sides a,b,c. Let c be the longest side.

We have three possible cases:

For this problem, we have a = 20, b = 23, c = 41.

We see that a^2+b^2 = 20^2+23^2 = 929 and c^2 = 41^2 = 1681.

In short, a^2+b^2 = 929 and c^2 = 1681.

Since 929 < 1681, this means a^2+b^2 < c^2.

Therefore, this triangle is obtuse.

n=9

step-by-step explanation:

7 times a number = 7n

decreased by 13 = 7n-13

same as is =

5 times the number = 5n

increased by 5 = 5n+5

7n-13 = 5n+5

2n=18

n=9