Question

solve for x using the figure to the right.
x = \boxed{\text{(simplify your answer. type an exact answer, using radicals as needed.)}}
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Explanation:

Step1: Identify geometric theorem

This is a right triangle altitude scenario: when an altitude is drawn to the hypotenuse of a right triangle, the length of the altitude is the geometric mean of the lengths of the two segments of the hypotenuse. The formula is $x = \sqrt{a \times b}$, where $a=40$ and $b=10$.

Step2: Substitute values into formula

$$x = \sqrt{40 \times 10}$$

Step3: Simplify the expression

$$x = \sqrt{400} = 20$$

Answer:

20