Question

Draw a kite that has a triangle with sides 1, 1, 2x next to a triangle with sides 2x, 2, 2. Find the area A and the x that maximizes it.

Answer 1

The area of the kite is
a = x(√(1-x^2) + √(4-x^2))

da/dx =
[√(1-x^2) + √(4-x^2)][√(1-x^2)√(4-x^2)-x^2]
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√(1-x^2)√(4-x^2

da/dx = 0 when x = 2/√5

Answer 2

thanks for your help