The altitude to the hypotenuse of a right triangle divides the hypotenuse into segments 6 inch and 10 inch long, Find the length h of the altitude.
To solve this problem, we can use the concept of similar triangles.
Let's call the altitude h. According to the problem, one segment of the hypotenuse is 6 inches, and the other segment is 10 inches.
We can set up a proportion to find the length of the entire hypotenuse. The proportion can be set up using the two segments of the hypotenuse and the whole hypotenuse:
(h / 6) = (10 / (6 + 10))
To solve for h, we can cross-multiply the proportion:
h = (6 * 10) / (6 + 10)
h = 60 / 16
h ≈ 3.75 inches
Thus, the length of the altitude, h, is approximately 3.75 inches.
To find the length "h" of the altitude, we can use the property that the length of an altitude of a right triangle is the geometric mean of the two segments it divides the hypotenuse into.
In this case, we are given that the hypotenuse is divided into two segments, one is 6 inches long (let's call it "a"), and the other is 10 inches long (let's call it "b").
So, we need to find the geometric mean between "a" and "b". The formula to find the geometric mean is:
h = √(a * b)
Now, let's substitute the given values into the formula:
h = √(6 * 10)
Simplifying:
h = √60
= √(2 * 2 * 3 * 5)
= 2√(3 * 5)
= 2√15
Therefore, the length "h" of the altitude is 2√15 inches.
the topic is discussed quite well at
http://jwilson.coe.uga.edu/emt668/emat6680.folders/brooks/6690stuff/righttriangle/rightday3.html