Question 203862
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