The altitude upon the hypotenuse of a right triangle divides the hypotnuse into segments of 3 and 12. find the length of the altitude
let that altitude be x
Can you see how that altitude splits your right-angled triangle into two smaller right-angled triangles which are similar?
so you can set up the ratio
12/x= x/3
x^2= 36
x = 6
The measure of the altitude drawn from the vertex of the right angle of a right triangle to its hypotenuse is the geometric mean between the measures of the two segments of the hypotenuse.
Triangle ABC, where A is the vertex, CB is the hypotenuse, and AD is the altitude.
AD = altitude, CD = 3, DB = 12
AD/DB = CD/AD
AD/12 = 3/AD
(AD)^2 = 36
AD = (sqrt(3 * 12))
AD = (sqrt(36))
AD = 6
Thanku sooo much!
Well, well, well, looks like we have ourselves a right triangle conundrum! So, the altitude splits the hypotenuse into two segments, with lengths of 3 and 12. Let's call the length of the altitude "x". Now, you might be wondering, "Clown Bot, how on Earth can we find the length of the altitude?"
Fear not, my friend, for I shall guide you through this challenge with my trusty comedic compass. We can use a little bit of Pythagoras to solve this puzzle. According to the Pythagorean theorem, in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
In our case, the hypotenuse is 15 units long (3 + 12 = 15). Now, let's say the length of the altitude is "x". We can write the equation as follows:
15² = 3² + x² + 12²
Now, let's crunch some numbers, shall we? 15² equals 225, 3² equals 9, and 12² equals 144. So we have:
225 = 9 + x² + 144
Now, by subtracting 9 and 144 from both sides, we get:
225 - 9 - 144 = x²
That gives us:
72 = x²
And voila! We have found our answer. The length of the altitude is the square root of 72. But please don't panic, I come bearing the solution – the length of the altitude is approximately 8.485 units. So, there you have it, my friend: the length of the altitude in this right triangle is approximately 8.485 units.
Now, doesn't that make math a bit more amusing?
To find the length of the altitude, we can use the Pythagorean theorem.
In a right triangle, the Pythagorean theorem states that the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
Let's denote the length of the altitude as 'h', and the lengths of the two segments on the hypotenuse as 'x' and 'y'.
From the problem, we know that x = 3 and y = 12.
Using the Pythagorean theorem, we have:
(x^2) + (h^2) = (y^2)
Substituting the values, we get:
(3^2) + (h^2) = (12^2)
Simplifying the equation, we have:
9 + (h^2) = 144
Subtracting 9 from both sides, we get:
h^2 = 135
To find the length of the altitude, we need to take the square root of both sides:
√(h^2) = √135
So, the length of the altitude (h) is approximately 11.62 units.