Find the maximal area of a right triangle with hypotenuse of length 5.

Question

Find the maximal area of a right triangle with hypotenuse of length 5.

Answer 1

K.M., the area of a triangle is: A= (1/2)(base)(height)

in this case, A= (1/2)(x)(sq rt.(25 - x²)-- thanks to the pythag. thm.

Now you can find the max value by finding where f'(x) = 0 and f"(x) is negative (so the function is concave down, so local max)

Just to be sure, you should always check the endpoints, where x = 0 and x = 5