Question

directions: state if the three side lengths form a right triangle.

1. 6, 8, 12
2. 9, 12, 15
3. 10, √69, 13
4. 2, √9, √14

directions: state if each triangle is acute, obtuse, or right.
12)

1. 5 ft

Explanation:

Problem 8: 6, 8, 12

Step1: Identify the longest side.

Longest side \( c = 12 \), so \( a = 6 \), \( b = 8 \).

Step2: Apply Pythagorean theorem.

Check \( a^2 + b^2 \) vs \( c^2 \).
\( a^2 + b^2 = 6^2 + 8^2 = 36 + 64 = 100 \)
\( c^2 = 12^2 = 144 \)

Step3: Compare values.

Since \( 100 < 144 \) (\( a^2 + b^2 < c^2 \)), the triangle is obtuse (not right).

Step1: Identify the longest side.

Longest side \( c = 15 \), so \( a = 9 \), \( b = 12 \).

Step2: Apply Pythagorean theorem.

Check \( a^2 + b^2 \) vs \( c^2 \).
\( a^2 + b^2 = 9^2 + 12^2 = 81 + 144 = 225 \)
\( c^2 = 15^2 = 225 \)

Step3: Compare values.

Since \( 225 = 225 \) (\( a^2 + b^2 = c^2 \)), the triangle is right.

Step1: Identify the longest side.

Longest side \( c = 13 \), so \( a = 10 \), \( b = \sqrt{69} \).

Step2: Apply Pythagorean theorem.

Check \( a^2 + b^2 \) vs \( c^2 \).
\( a^2 + b^2 = 10^2 + (\sqrt{69})^2 = 100 + 69 = 169 \)
\( c^2 = 13^2 = 169 \)

Step3: Compare values.

Since \( 169 = 169 \) (\( a^2 + b^2 = c^2 \)), the triangle is right.

Answer:

Not a right triangle (obtuse).

Problem 9: 9, 12, 15