Answer:
<em>The maximum area of the second board must be square inches.</em>
Step-by-step explanation:
The total area of two different size boards cannot exceed square inches.
The area of one board is square inches.
Suppose, the area of the second board is square inches.
That means......
So, the maximum area of the second board must be square inches.
so we have three points, A, B and C, if indeed AC is the diameter of the circle, then half the distance of AC is its radius, and the midpoint of AC is the center of the circle, morever, since B is also on the circle, the distance from B to the center must be the same radius distance.
in short, half the distance of AC must be equals to the distance of B to the midpoint of AC, if indeed AC is the diameter.
now, let's check the distance from say A to the center, and check the distance of B to the center, if it's indeed the center, they'll be the same and thus AC its diameter.