In a tile model, a square of side (u+v) is divided into a square of area u², a square of area v², and two equal rectangles. What is the area of each rectangle?

Correct answer: uv

The correct answer is C: each rectangle has area uv. Start with the basic rule that the area of a rectangle equals length × breadth. In the square model, one side of each smaller rectangle has length u and the other has length v. Therefore, the area of one rectangle is u × v = uv. There are two such rectangles, so together they contribute uv + uv = 2uv; however, the question asks for each rectangle separately, so the answer is only uv. Option A, (u+v)², is the area of the entire large square, not one rectangle. Option B, u²v², incorrectly multiplies the areas of the two square pieces and also has the wrong dimensions. Option D, 2uv, is the combined area of both rectangles, not the area of one. Memory cue: one rectangle gives uv; two equal rectangles give 2uv.