Question

1. solve for x

10.8
6√7
20
10

Explanation:

Step1: Apply geometric - mean theorem

In a right - triangle with an altitude drawn to the hypotenuse, if the lengths of the segments of the hypotenuse are \(a = 4\) and \(b = 9\), and the length of the altitude is \(h\), and the length of the side we want to find \(x\) is related to the segments of the hypotenuse by the formula \(x^{2}=b(a + b)\) (or by the geometric - mean relationships). Here, we use the fact that if we consider the right - triangle formed by the altitude and the two sub - segments of the hypotenuse, we know that \(x^{2}=9\times(4 + 9)\).

Step2: Calculate the value of \(x^{2}\)

\[x^{2}=9\times13=117\]

Step3: Find the value of \(x\)

\[x=\sqrt{117}=3\sqrt{13}\approx 10.8\]

Answer:

10.8