The figure above is a right triangle with sides x, 3 cm, and x√3 cm.
Since it is a right triangle, we can use the Pythagorean theorem to find the value of x. The theorem states that the sum of the squares of the two shorter sides of a right triangle is equal to the square of the longest side, which is the hypotenuse.
So, we have:
x^2 + (3)^2 = (x√3)^2
Expanding the square on the right side:
x^2 + 9 = x^2 * 3
Simplifying the equation:
x^2 + 9 = 3x^2
Solving for x:
2x^2 = 9
x^2 = 4.5
Taking the square root of both sides:
x = ±√(4.5)
Since x has to be positive, we choose the positive square root:
x = √(4.5) = 2√3
Finally, multiplying by 10:
x = 10√3
So, the value of x in the figure is 10√3 cm.
