Final Answer:
The value of (m) in the geometric mean (altitude) theorem is c) 20.
Step-by-step explanation:
In the geometric mean (altitude) theorem, the altitude of a right-angled triangle is the geometric mean between the segments it divides on the hypotenuse. The formula for calculating the altitude (m) is m = √(a b), where a and b are the segments of the hypotenuse. Given that m = 20, we can find the segments a and b using the formula m = √(a b).
By squaring both sides of the equation, we get 400 = a * b. To find the values of a and b, we can use the options provided. By testing each option, we find that when a = 20 and b = 20, their product equals 400, satisfying the equation. Therefore, the value of (m) is 20.
The geometric mean (altitude) theorem is a fundamental concept in geometry, particularly in trigonometry and Pythagorean theorem applications. It provides a method for finding the altitude of a right-angled triangle when given the lengths of its hypotenuse segments.
In this case, by applying the formula m = √(a * b), we were able to determine that m equals 20 by finding two segments whose product equals 400. This demonstrates how the theorem can be used to solve for unknown values in right-angled triangles.
In conclusion, by understanding and applying the geometric mean (altitude) theorem, we were able to calculate the value of (m) as 20 in this particular right-angled triangle scenario. This theorem is essential for solving various problems related to right-angled triangles and provides a clear method for determining altitudes based on segment lengths.
So correct option is c) 20.