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.
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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.
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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
