Find the maximal area of a right triangle with hypotenuse of length 3.

Answer 1

max area is (3 x 3)/2 = 9/2

draw a hypotenuse at a -45 degree angle, slope=-1. line segment from y intercept to x intercept, from (0,3) to (3,0), line through the intercepts is: y=-x+3

area = hb/2 = xy/2 = (3)(3)/2 = 9/2 = 4.5

this is basicaly the same microeconics problem of finding the revenue maximing point, for a linear demand curve. It's the midpoint, with unit elasticity. (3/2,3/2) It's a vertex of an inscribed rectangle or square with sides 3/2 and 3/2. add up all the area under the demand curve to get 2(3/2)(3/2) = 9/2

Answer 2

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