Applications of Derivatives
Maxima and Minima
Grade 12
Question:
<p>Consider a trapezoid ABCD with AB = 8 cm perpendicular to the base, BC = 6 cm and AD = 10 cm. The maximum possible area of rectangle inscribed in the trapezoid so that one of its sides lies on the larger base of trapezoid is:</p>
<p>(a) 36</p>
<p>(b) 54</p>
<p>(c) 42</p>
<p>(d) 48</p>
Step-by-Step Solution
Key Concept: Set up coordinates with the trapezoid positioned appropriately. Let the rectangle have one side on the base AD. Use similar triangles or parametric equations to express area as a function of height and optimize.
<p>Not provided in source material.</p>
Correct Answer: D