2008 iTest Problems/Problem 6
Problem
Let be the length of the altitude to the hypotenuse of a right triangle with legs 5 and 12. Find the least integer greater than .
Solution
By the Pythagorean Theorem, the hypotenuse will be . The area of this triangle can be expressed in 2 ways: half the product of the legs, and half the product of the hypotenuse and its altitude. We can easily find the area using the first method: . Therefore, we have . Multiplying both sides by and dividing both sides by , we get . The least integer greater than is .
See Also
2008 iTest (Problems) | ||
Preceded by: Problem 5 |
Followed by: Problem 7 | |
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