Question

Determine whether the triangle with the given side lengths is a right triangle. (a^2 + b^2 = c^2) 8 meters, 10 meters, 12 meters

a) Yes
b) No

Answer 1

By applying the Pythagorean theorem to the triangle with side lengths of 8 meters, 10 meters, and 12 meters, we find that the triangle is indeed a right triangle since 8² + 10² matches 12².

Step-by-step explanation:

To determine whether a triangle with side lengths of 8 meters, 10 meters, and 12 meters is a right triangle, we apply the Pythagorean theorem, which states that for a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b), or a² + b² = c². Here, if we assume that 12 meters is the length of the hypotenuse, our equation would be 8² + 10² = 12². Calculating each side, we get 64 + 100 = 144, which equals 12². However, 12² is 144, so the equation holds true, hence the triangle is a right triangle.