In a square tile model, the central square is (9a²), the combined area of two equal strips is (30ab), and the small square is (25b²). What is the side of the whole square?

Correct answer: (3a+5b)

The direct answer is option A: 3a + 5b. The central square has area 9a², so its side is √(9a²) = 3a, taking the usual nonnegative lengths. The small square has area 25b², so its side is √(25b²) = 5b. In the tile arrangement, these side lengths join along the outer side of the complete square, so the whole side is 3a + 5b. The two equal strips provide a useful check: their total area is 2(3a)(5b) = 30ab, exactly as given. Option B uses the square areas as though they were side lengths. Option C uses subtraction, which would describe a difference arrangement rather than the stated joined tiles. Option D reverses the coefficients and does not give the sides of the two stated squares in the required order. Memory cue: take square roots of the corner-square areas, then add the adjacent side lengths.