Could the following set of side lengths form a right triangle? Explain
2, 4, 5
Yes, because the given numbers do not satisfy the equation a ^ 2 + b ^ 2 = c ^ 2
Yes, because given sumbers satisfy the equation a ^ 2 + b ^ 3 = c ^ 2
No, betause the given numbers satisfy the equation a ^ 2 + b ^ 2 = c ^ 2
No, because the given do not satisfy the equation a ^ 2 + b ^ 2 = c ^ 2
4 + 16 is NOT 25 so this is NOT a right triangle.
No, the given set of side lengths (2, 4, 5) cannot form a right triangle. This can be determined by using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
If we denote the sides of the triangle as a, b, and c, where c is the hypotenuse, the Pythagorean theorem can be written as:
a^2 + b^2 = c^2
In this case, the given side lengths are 2, 4, and 5. So, plugging these values into the equation:
2^2 + 4^2 = 5^2
4 + 16 = 25
20 does not equal 25, so the equation is not satisfied. Therefore, the given set of side lengths cannot form a right triangle.
The equation a^2 + b^2 = c^2 is known as the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two shorter sides (a and b) is equal to the square of the length of the longest side (c).
To determine if the given set of side lengths (2, 4, 5) can form a right triangle, we substitute the side lengths into the Pythagorean theorem equation.
Here, a = 2, b = 4, and c = 5.
a^2 + b^2 = c^2
2^2 + 4^2 = 5^2
4 + 16 = 25
20 ≠ 25
Since the equation does not hold true, the given set of side lengths (2, 4, 5) cannot form a right triangle. Therefore, the correct answer is "No, because the given numbers do not satisfy the equation a^2 + b^2 = c^2."