Question

in exercises 1–4, determine whether a triangle with the given side lengths is a right triangle. 1. 76, 120, 98 2. 221, 204, 85 3. 5.0, 1.4, 4.8 4. 80, 82, 18

Explanation:

Problem 1: 76, 120, 98

Step1: Identify the longest side

The longest side is 120. So, we check if \(76^2 + 98^2 = 120^2\).

Step2: Calculate each square

\(76^2 = 5776\), \(98^2 = 9604\), \(120^2 = 14400\).

Step3: Sum the squares of the shorter sides

\(5776 + 9604 = 15380\).

Step4: Compare with the square of the longest side

Since \(15380
eq 14400\), it is not a right triangle.

Problem 2: 221, 204, 85

Step1: Identify the longest side

The longest side is 221. Check if \(204^2 + 85^2 = 221^2\).

Step2: Calculate each square

\(204^2 = 41616\), \(85^2 = 7225\), \(221^2 = 48841\).

Step3: Sum the squares of the shorter sides

\(41616 + 7225 = 48841\).

Step4: Compare

Since \(48841 = 48841\), it is a right triangle.

Problem 3: 5.0, 1.4, 4.8

Step1: Identify the longest side

The longest side is 5.0. Check if \(1.4^2 + 4.8^2 = 5.0^2\).

Step2: Calculate each square

\(1.4^2 = 1.96\), \(4.8^2 = 23.04\), \(5.0^2 = 25.0\).

Step3: Sum the squares of the shorter sides

\(1.96 + 23.04 = 25.0\).

Step4: Compare

Since \(25.0 = 25.0\), it is a right triangle.

Problem 4: 80, 82, 18

Answer:

s:

1. Not a right triangle.
2. Right triangle.
3. Right triangle.
4. Right triangle.