Answer:
To form a right triangle, one of the sides of the triangle must be the hypotenuse and the other two sides must be the legs. The hypotenuse is the longest side of a right triangle and the side opposite the right angle. In this case, the side with length 5x is the hypotenuse. Therefore, the sides with lengths 3x and 24 must be the legs.
We can use the Pythagorean Theorem to determine the value of x that will make this a right triangle. The Pythagorean Theorem states that 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. In this case, we have:
5x^2 = 3x^2 + 24^2
Solving for x, we get:
x = sqrt(24^2/(5^2 - 3^2)) = sqrt(576/16) = 6
Therefore, a value of x = 6 will make this a right triangle.
Explanation: