Which shaded triangle is a right triangle? Explain.

Question

Choose the correct answer below.
A. Triangle XYZ is a right triangle because 16² + (√105)² = (√361)²
B. Triangle ABC is a right triangle because (√16)² + (√105)² = (√361)²
C. Triangle XYZ is a right triangle because (√16)² + (√105)² = (√361)²
D. Triangle ABC is a right triangle because (√16)² + 105² = 361².

Quizzma Team · Answer

Let’s break down the options using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

1. Option A: Triangle XYZ is a right triangle because (16² + (√105)² = (√361)²).

– Calculate: (16² = 256), ((√105)² = 105), ((√361)² = 361).

– So, (256 + 105 = 361), which is correct.

2. Option B: Triangle ABC is a right triangle because ((√16)² + (√105)² = (√361)²).

– Calculate: ((√16)² = 16), ((√105)² = 105), ((√361)² = 361).

– So, (16 + 105 ≠ 361); this is incorrect.

3. Option C: Triangle XYZ is a right triangle because ((√16)² + (√105)² = (√361)²).

– This is the same calculation as in Option B; it is incorrect as shown above.

4. Option D: Triangle ABC is a right triangle because ((

Which shaded triangle is a right triangle? Explain.

1 Answer