Question

calculator
what is the value of x?
round to the nearest tenth, if necessary.
x = 6
x = 6.3
x = 7
x = 9.2

Explanation:

Step1: Recall Geometric Mean Theorem

In a right triangle, the altitude to the hypotenuse is the geometric mean of the segments into which it divides the hypotenuse. So, \(x = \sqrt{DC\times CB}\).

Step2: Substitute Values

Given \(DC = 10\) and \(CB = 4\), substitute into the formula: \(x=\sqrt{10\times4}=\sqrt{40}\).

Step3: Calculate and Round

\(\sqrt{40}\approx6.3245\), rounding to the nearest tenth gives \(x\approx6.3\).

Answer:

B. \(x = 6.3\)