the altitude, AD, to the hypotenuse BC of right triangle ABC divides the hypotenuse into segments that are 8 and 10 cm long. find the length of the altitude.
Let's call the length of the altitude AD as x.
According to the problem, AD divides the hypotenuse BC into segments that are 8 cm and 10 cm long.
Using the Pythagorean Theorem, we can set up an equation using the lengths of the segments on the hypotenuse:
BD^2 + CD^2 = BC^2
Replacing BD with 8 cm and CD with 10 cm, we get:
8^2 + x^2 = 10^2
Simplifying the equation, we have:
64 + x^2 = 100
Subtracting 64 from both sides, we get:
x^2 = 36
Taking the square root of both sides, we have:
x = √36
x = 6
So, the length of the altitude AD is 6 cm.
To find the length of the altitude, we can use the property of similar triangles in right triangles.
Let's label the length of the altitude AD as x.
According to the given information, the segments BD and DC are 8 cm and 10 cm long, respectively.
We can set up the following proportion using the lengths of the segments:
BD/AD = AD/DC
Substituting the given values, we have:
8/x = x/10
To solve this proportion, we can cross-multiply:
8 * 10 = x * x
80 = x^2
Taking the square root of both sides, we get:
√80 = x
Simplifying the square root of 80, we have:
x ≈ 8.94
Therefore, the length of the altitude AD is approximately 8.94 cm.