SOLUTION: Sam, a modern artist, has submitted a sketch of a proposed piece to a client who wants s simple, clean - lined decoration to place in the lobby of a new office building. Sam’s

Question 1155270: Sam, a modern artist, has submitted a sketch of a proposed piece to a client who wants s simple, clean - lined decoration to place in the lobby of a new office building. Sam’s sketch shows an eight - foot column whose cross section is a right triangle, so the column has three plane surfaces. The client commissions Sam to do the work, but stipulates that the hypotenuse of the triangle must be 40 inches and triangular cross - sectional area is maximized. What dimensions should be used for two sides of the right triangle if these stipulations are to be met? Recall that the area of a right triangle is one-half the products of the lengths of the sides, and the sum of the squares of the sides equals the square of the hypotenuse. State your answer to the nearest one - hundredth of an inch.
Answer by ikleyn(52786) (Show Source): You can put this solution on YOUR website!
.


Consider right angled triangle with the hypotenuse of 40 inches long.


Circumscribe the circle about this triangle.


Then the hypotenuse is the diameter of this circle.


It is absolutely clear/obvious then, that the maximum height will be provided by the perpendicular to the diameter, 
erected from its middle point (which is the center of the circle)


It means that the triangle which provides the maximum area, is the ISOSCELES right angled triangle with the hypotenuse of the given length.


So, the answer is: the legs of this triangle must be    inches

and its area is then   =  = 40*10 = 400 square inches.

Solved.

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