Answer & Step-by-step explanation:
To determine if a triangle is a right triangle, we can use the Pythagorean theorem. The Pythagorean theorem states that 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 apply the Pythagorean theorem to the given triangle with sides of lengths 39 meters, 43 meters, and 61 meters:
a^2 + b^2 = c^2
Where a and b are the lengths of the two shorter sides, and c is the length of the hypotenuse.
Plugging in the values:
39^2 + 43^2 = 61^2
Simplifying:
1521 + 1849 = 3721
3370 ≠ 3721
Since the sum of the squares of the two shorter sides is not equal to the square of the hypotenuse, the given triangle is not a right triangle.
Therefore, based on the lengths of the sides, we can conclude that the triangle is not a right triangle.
hope this helps.