How do you find the right triangle of maximum area if the sum of the lengths of the legs is 5?

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Answer 1 · 2015-06-07T04:37:51

Call x and y the 2 legs.

Area of the right triangle: #s = (x.y)/2#

Given: x + y = 5 --> y = 5 - x

Then, #s = x/2(5 - x) = -(1/2)(x^2 - 5x)#

s maximum when the derivative s' = 0 -> 2x - 5 = 0 --># x = 5/2#.

The area is max when both legs are equals.# x = y = 5/2#

#s max = (1/2)(5/2)(5/2) = 25/8#

Check:

When x = 2, y = 3, the area is #s = (2(3))/2 = # 3
When x = 1, and y = 4, the area is #s = (1/2)(4) = 2#