7) Of all the triangles with sides measuring $4, 5, x$, the one with the maximum area will have $x$ equal to
(A) 4
(B) 5
(C) 4.5
(D) $\sqrt{20}$
(E) $\sqrt{41}$.
7) The answer is _e_ _E_

Let's call, for example, the base of the triangle the side of length 4. The area of the triangle is equal to 2 multiplied by its height; on the other hand, the height is less than or equal to 5, which is the length of another side. The equality between these two quantities, and therefore the maximum area, occurs when the two sides of lengths 4 and 5 are perpendicular. Applying the Pythagorean theorem, we get $x=\sqrt{5^{2}+4^{2}}=\sqrt{41}$.