what is the value of x?\n2 units\n3 units\n5 units\n8 units

Answer

Explanation:

Step1: Apply geometric - mean theorem

In a right - triangle, if an altitude is drawn from the right - angle vertex to the hypotenuse, then the altitude is the geometric mean between the segments of the hypotenuse. So, we have the equation $10^{2}=x\times4x$.

Step2: Simplify the equation

$100 = 4x^{2}$.

Step3: Solve for $x^{2}$

Divide both sides of the equation by 4: $x^{2}=\frac{100}{4}=25$.

Step4: Solve for $x$

Take the square root of both sides. Since $x$ represents a length, we consider the positive square root. So, $x = 5$.

Answer:

5 units