SOLUTION: The altitude drawn to the hypotenuse of a right triangle divides the hypotenuse into two segments, whose lengths are 8" and 18". How long is the altitude?
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Question 149702: The altitude drawn to the hypotenuse of a right triangle divides the hypotenuse into two segments, whose lengths are 8" and 18". How long is the altitude?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
First, let's draw the picture. Be sure you label every length you can
So we can see that the hypotenuse of the largest triangle is 26 units. Using pythagoreans theorem, we get:
Now looking at the left most smaller triangle, we see that the legs are 8 and "h" while the hypotenuse is "x". So once again, with pythagoreans theorem, we can say:
Now solving for , we get
Finally, the right most smaller triangle has a base of 18 and "h" and a hypotenuse of y. So this gives us:
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Start with the first equation.
Plug in . In other words, replace with
Square 18 to get 324. Square 26 to get 676.
Square 18 to get 324. Square 26 to get 676.
Plug in
Square 8 to get 64
Combine like terms.
Subtract 260 from both sides.
Divide both sides by 2.
Take the square root of both sides. Note: only the positive square root is considered.
So the length of x is which is about 14.422 units (this isn't important).
Go back to the second equation
Plug in
Square the square root to eliminate it.
Square 8 to get 64
Combine like terms.
Take the square root of both sides. Once again, only the positive square root is considered.
So the height is 12 units which means that altitude is 12 units.
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