find the largest possible area for a right angled triangle if the hypotenuse is the square root of 1-x long and the base is is the square root of x long

Question

find the largest possible area for a right angled triangle if the hypotenuse is the square root of  1-x long and the base is is the square root of x long

anonymous · Answer

Hi pmats...I'm not sure why it's asking you to find the "largest possible area" when there is only "one" area of a right triangle...but anyway...this is how you do it...use the Pythagorean formula a^2 +b^2 = c^2...
you gave the hypotenuse as 1-x so let c = (1-x)...then let a = root(x)...
your Pythagorean formula would then be (root(x))^2 + b^2 = (1-x)^2...
now just solve for b...since the formula for the area of a triangle is 1/2base times height, your base is rootx and height is "b"...look at the attached work to see the final answer...hope this helps! Good luck!

anonymous · Answer

attachment