Question

Do the following side lengths, 24, 32, and 2√10, form an acute, right, or obtuse triangle? Justify your answer by showing your work.

A) Acute triangle; the sum of the squares of the shorter sides is greater than the square of the longest side.
B) Right triangle; the sum of the squares of the shorter sides is equal to the square of the longest side.
C) Obtuse triangle; the sum of the squares of the shorter sides is less than the square of the longest side.
D) None of the above.

Answer 1

The side lengths 24, 32, and 2√10 form an acute triangle.

Step-by-step explanation:

To determine whether the side lengths 24, 32, and 2√10 form an acute, right, or obtuse triangle, we need to check the relationship between the squares of the shorter sides and the square of the longest side. Let's calculate:

The square of 24 is 576, the square of 32 is 1024, and the square of 2√10 is 80. Adding the squares of the shorter sides, we get 576 + 1024 = 1600.

The square of the longest side is 80, which is less than 1600. Therefore, the sum of the squares of the shorter sides is greater than the square of the longest side, indicating that these side lengths form an acute triangle.