Question

Determine the length of a ladder that Sir Gleefulheart needs to reach the top

of the battlement (castle) to the nearest meter if the moat (water)
surrounding the battlement is 6 meters wide. The top of the battlement is 8
meters above the moat. *

Answer 1

9514 1404 393

Answer:

10 meters

Explanation:

You recognize that the ratio of leg lengths of the right triangle involved is ...

6 : 8 = 3 : 4

You know that any right triangle with leg lengths 3 and 4 has a hypotenuse of 5. The ladder will need to be in the same ratio:

3 : 4 : 5 = 6 : 8 : 10

The ladder needs to be 10 meters long.

_____

In case you don't remember that (3, 4, 5) is a "Pythagorean triple," you can figure the length using the Pythagorean theorem.

6^2 +8^2 = hypotenuse^2

36 +64 = 100 = hypotenuse^2

hypotenuse = √100 = 10 . . . . required ladder length in meters