Question

Which of the following sets of measures for the sides of a triangle forms a right triangle, where the Pythagorean Theorem (a² + b² = c²) must hold, and the largest side must be the hypotenuse (c)?

A) 41 cm, 40 cm, 9 cm
B) 45 ft, 40 ft, 35 ft
C) 52 in, 50 in, 11 in
D) 45 yd, 35 yd, 25 yd

Which option is correct?

A
B
C
D

Answer 1

The correct set of measures for the sides of a right triangle, where the Pythagorean theorem holds, and the largest side is the hypotenuse, is option C) 52 in, 50 in, 11 in

Step-by-step explanation:

The triangle that represents a right triangle and satisfies the Pythagorean theorem is option D) 45 yd, 35 yd, 25 yd. To determine if a triangle is a right triangle, we need to check if the square of the longest side (hypotenuse) is equal to the sum of the squares of the other two sides. In option D, we have:

a = 45 yd, b = 35 yd, c = 25 yd

Using the Pythagorean theorem: a² + b² = c²
45² + 35² = 25²
2025 + 1225 = 625
3250 = 625

The equation 3250 = 625 is not true, so option D does not satisfy the Pythagorean theorem. Hence, the correct option is C) 52 in, 50 in, 11 in which forms a right triangle since 52² + 50² = 11². Therefore, the hypotenuse of this triangle is the longest side of the triangle.