Question

Determine whether each set of numbers can be the measure of the sides of a triangle. If so, classify the triangle as acute, right, or obtuse. Justify your answer.
b. 2 √3, 4√2, 3 √5

Answer 1

The following set of numbers 2√3, 4√2, and 3√5, 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 = 2√3, b = 4√2, and c = 3√5

a + b > c     2√3 + 4√2 > 3√5     9.12 > 6.71     True

a + c > b     2√3 + 3√5 > 4√2     10.17 > 5.66    True

b + c > a     4√2 + 3√5 > 2√3     12.37 > 3.46     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.

(2√3)^2 + (4√2)^2 = 44

2. Compare it to the square of the largest side.

(3√5)^2 = 45

44 < 45

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, 2√3, 4√2, and 3√5 can be the measure of the sides of an obtuse triangle.

To learn more about types of triangle based on side lengths: brainly.com/question/13619935

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