Question

The hypotenuse of a right triangle has a length of √200 units. Find the length of the other two sides that maximize the area.

Answer 1

Answer
W = width L = height H = hypotenuse
W^2 + L^2 = 200
dW / dL = -L differentiate wrt L (I)
A = 1/2 W L
W + L dW / dL = 0 to find max area
dW / dL = - W / L (II)
W = L^2 combining (I) and (II)
L^4 + L^2 = 200
Let x = L^2
x^2 + x - 200 = 0
x = 13.65 solve quadratic
L = 3.69
W = 13.65
(L * W) / 2 = 25.2 Area of triangle
L^2 + W^2 = 3.69^2 + 13.65^2 = 200