Question

determine whether the triangle with the given side length is a right triangle
17 9,12,15
18 24, 27.5, 36.5
19 3, 5, 6
20 6, 12, 13

Explanation:

Problem 17: Sides 9, 12, 15

Step1: Identify the hypotenuse (longest side)

The longest side is 15. So, we check if \(9^2 + 12^2 = 15^2\).

Step2: Calculate the squares

\(9^2 = 81\), \(12^2 = 144\), \(15^2 = 225\).

Step3: Sum the squares of the shorter sides

\(81 + 144 = 225\).

Step4: Compare with the square of the longest side

Since \(81 + 144 = 225 = 15^2\), by the Pythagorean theorem, it is a right triangle.

Problem 18: Sides 24, 27.5, 36.5

Step1: Identify the hypotenuse (longest side)

The longest side is 36.5. Check if \(24^2 + 27.5^2 = 36.5^2\).

Step2: Calculate the squares

\(24^2 = 576\), \(27.5^2 = 756.25\), \(36.5^2 = 1332.25\).

Step3: Sum the squares of the shorter sides

\(576 + 756.25 = 1332.25\).

Step4: Compare with the square of the longest side

Since \(576 + 756.25 = 1332.25 = 36.5^2\), by the Pythagorean theorem, it is a right triangle.

Problem 19: Sides 3, 5, 6

Step1: Identify the hypotenuse (longest side)

The longest side is 6. Check if \(3^2 + 5^2 = 6^2\).

Step2: Calculate the squares

\(3^2 = 9\), \(5^2 = 25\), \(6^2 = 36\).

Step3: Sum the squares of the shorter sides

\(9 + 25 = 34\).

Step4: Compare with the square of the longest side

Since \(34
eq 36\), by the Pythagorean theorem, it is not a right triangle.

Problem 20: Sides 6, 12, 13

Answer:

s:

• Problem 17: Yes (it is a right triangle)
• Problem 18: Yes (it is a right triangle)
• Problem 19: No (it is not a right triangle)
• Problem 20: No (it is not a right triangle)