If triangle DEF has sides measuring 50, 40, and 32, is the triangle a right triangle? If it is a right triangle, answer with the number 90. If it is not a right triangle, answer with the number 0.(1 point)

Question

If triangle DEF has sides measuring 50, 40, and 32, is the triangle a right triangle? If it is a right triangle, answer with the number 90. If it is not a right triangle, answer with the number 0.(1 point)

Answer 1

To determine if the triangle is a right triangle, we can use the Pythagorean theorem. According to the theorem, in a right triangle, the square of the length of the longest side (hypotenuse) is equal to the sum of the squares of the other two sides.

In this case, the longest side has a length of 50.
The other two sides have lengths of 40 and 32.

Using the Pythagorean theorem:

50^2 = 40^2 + 32^2
2500 = 1600 + 1024
2500 ≠ 2624

Since the equation is not true, it means that the triangle DEF is not a right triangle. Therefore, the answer is 0.

Answer 2

To determine if triangle DEF is a right triangle, we can use the Pythagorean theorem. According to the Pythagorean theorem, in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Let's calculate:

The longest side in triangle DEF is 50.
The other two sides are 40 and 32.

According to the Pythagorean theorem:
50^2 = 40^2 + 32^2

Simplifying:
2500 = 1600 + 1024

2500 = 2624

Since 2500 is not equal to 2624, triangle DEF is not a right triangle.

Therefore, the answer is 0.

Answer 3

To determine whether triangle DEF is a right triangle, we can use the Pythagorean theorem. According to the theorem, in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

In this case, the three sides of triangle DEF have lengths 50, 40, and 32. We can check if this relationship holds:

Using the Pythagorean theorem:

a² + b² = c²

(50)² + (40)² = (32)²

2500 + 1600 = 1024

4100 = 1024

Since 4100 is not equal to 1024, which is the square of any integer, the lengths given in the question do not form the sides of a right triangle.

Therefore, the triangle DEF is not a right triangle, and the answer is 0.

Answer 4

If triangle DEF has sides measuring 50, 40, and 32, is the triangle a right triangle? If it is a right triangle, answer with the number 90. If it is not a right triangle, answer with the number 0.(1 point)

To determine if the triangle is a right triangle, we can use the Pythagorean theorem. According to the theorem, in a right triangle, the square of the length of the longest side (hypotenuse) is equal to the sum of the squares of the other two sides.

To determine if triangle DEF is a right triangle, we can use the Pythagorean theorem. According to the Pythagorean theorem, in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

To determine whether triangle DEF is a right triangle, we can use the Pythagorean theorem. According to the theorem, in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Are you sure the answer is 0? :)