SOLUTION: I would appreciate your help, What are the sides of the rectangle with the largest area that can be inscribed in a right triangle whose sides are 6, 8 and 10 meter.

Question 203862: I would appreciate your help,
What are the sides of the rectangle with the largest area that can be inscribed in a right triangle whose sides are 6, 8 and 10 meter.
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
picture the right-angle at the origin with the 6m side on the x-axis and the 8m side on the y-axis

the corner of the rectangle opposite the origin lies on the hypotenuse at a point (x,y)
the equation of the hypotenuse is y = -4/3 x + 8

the area of the rectangle is the product of the corner dimensions ___ A = x * y

substituting ___ A = -4/3 x^2 + 8x

the maximum value lies on the axis of symmetry of the quadratic
x = -b / 2a ___ x = -8 / (2 * -4/3) ___ x = 3

substituting for y ___ y = -4/3 (3) + 8 = 4

so the sides of the rectangle are 3m and 4m
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