could 4 m 5 m 6 m be the sides of a right triangle

Answer 1

To determine whether the sides measuring 4m, 5m, and 6m can form a right triangle, we can use the Pythagorean theorem. The Pythagorean theorem states that for any 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 check if these given side lengths satisfy the theorem:

Assume that the sides 4m and 5m are the legs (a and b) and 6m is the hypotenuse (c). According to the Pythagorean theorem:

a^2 + b^2 = c^2

Plugging in the values:

4^2 + 5^2 = 6^2
16 + 25 = 36
41 ≠ 36

Since 41 is not equal to 36, this set of side lengths does not satisfy the Pythagorean theorem for a right triangle. Therefore, sides measuring 4m, 5m, and 6m cannot form a right triangle.