Question

(a) One triangle has side lengths 16, 18, and 5.

Compute the sum of the squares of the shorter lengths
5² +16²
= 281
Compute the square of the longest length.
18 = 324
What kind of triangle is it?
CAcute triangle
Right triangle
Cobtuse triangle

Answer 1

acute

Explanation:

To determine what kind of triangle it is, we need to compare the sum of the squares of the two shorter lengths (281) with the square of the longest length (324).

Since the sum of the squares of the two shorter sides (281) is less than the square of the longest side (324), we have the following relationships:

If the sum of the squares of the two shorter sides is less than the square of the longest side, it's an acute triangle.

If the sum of the squares of the two shorter sides is equal to the square of the longest side, it's a right triangle.

If the sum of the squares of the two shorter sides is greater than the square of the longest side, it's an obtuse triangle.

In this case, 281 is less than 324, so the triangle is an Acute Triangle.