in the figure below, find the exact value of y. (do not approximate your answer.)
in the figure below, find the exact value of y. (do not approximate your answer.)
Answer
Explanation:
Step1: Use geometric - mean theorem
In a right - triangle, if an altitude is drawn from the right - angle vertex to the hypotenuse, then the length of the altitude is the geometric mean between the lengths of the two segments of the hypotenuse. Also, the square of a leg is equal to the product of the hypotenuse and the segment of the hypotenuse adjacent to that leg. Let the hypotenuse be (y), one segment of the hypotenuse be (3), and the leg be (6). According to the leg - hypotenuse relationship in a right - triangle with an altitude drawn from the right - angle to the hypotenuse: (6^{2}=3\times y).
Step2: Solve for (y)
We have the equation (36 = 3y). Divide both sides of the equation by (3): (y=\frac{36}{3}).
Answer:
(12)