Question

using algebra find the value of each variable.
25.
triangle with segments 3, 9, and x, and right angles as shown

Explanation:

Step1: Identify geometric relationship

In a right triangle, the length of the altitude to the hypotenuse is the geometric mean of the lengths of the two segments it divides the hypotenuse into. The hypotenuse segments are 3 and 9, so:
$$x = \sqrt{3 \times 9}$$

Step2: Simplify the expression

Calculate the product inside the square root first, then take the square root:
$$x = \sqrt{27} = 3\sqrt{3}$$

Answer:

$3\sqrt{3}$