A triangle has sides of lengths 9 cm, 40 cm, and 41 cm. Which statement is true about this triangle?
Not a right triangle?
a^2 + b^2 = c^2,
(9)^2 + (40)^2 = (41)^2,
81 + 1600 = 1681,
1681 = 1681.
Therefore, this is a rt. triangle.
Right.
To determine whether a triangle is a right triangle, we need to check if it satisfies the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the lengths of the sides are given as 9 cm, 40 cm, and 41 cm. Let's check if the Pythagorean theorem holds:
9^2 + 40^2 = 81 + 1600 = 1681
41^2 = 1681
Since both sides of the equation are equal, we can conclude that the triangle satisfies the Pythagorean theorem. Therefore, the triangle with side lengths 9 cm, 40 cm, and 41 cm is a right triangle.
Hence, the statement "Not a right triangle" is not true for this triangle.