Respuesta :
The following set of numbers, 20, 21 and 31, can be the measures of the sides of an obtuse triangle.
A triangle is a polygon with three sides and three vertices.
To know if a set of number is a valid measure of the sides of a triangle, it must follow the Triangle Inequality Theorem which states that the sum of any two sides must be greater than the third side, such that a + b > c, a + c > b, and b + c > a.
let a = 20, b = 21, and c = 31
a + b > c 20 + 21 > 31 41 > 31 True
a + c > b 20 + 31 > 21 51 > 21 True
b + c > a 21 + 31 > 21 52 > 20 True
To know what type of triangle based on the length of its side:
1. Take the sum of the squares of the two smaller sides.
20^2 + 21^2 = 841
2. Compare it to the square of the largest side.
31^2 = 961
961 > 841
If the sum of the squares of the 2 is larger than the square of the 3rd, it is an acute triangle.
if they are equal, it is a right triangle
if they are smaller, then it is an obtuse triangle.
Hence, 20, 21 and 31 can be the measure of the sides of an obtuse triangle.
To learn more about types of triangle based on side lengths: https://brainly.com/question/13619935
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