1. **State the problem:** We have an unshaded rectangle with perimeter 10 cm, height 3 units, width 2 units, and a larger shaded rectangle formed by joining two copies of the unshaded rectangle side by side. 2. **Find the perimeter of the unshaded rectangle:** The formula for perimeter of a rectangle is $$P = 2(\text{height} + \text{width})$$ Given the unshaded rectangle has perimeter 10 cm, so: $$10 = 2(h + w)$$ 3. **Check the given dimensions:** Height $h = 3$ units, width $w = 2$ units. Calculate perimeter: $$P = 2(3 + 2) = 2 \times 5 = 10$$ This matches the given perimeter. 4. **Find dimensions of the shaded rectangle:** Two unshaded rectangles joined side by side horizontally means: - Height remains the same: $3$ units - Width doubles: $2 \times 2 = 4$ units 5. **Calculate perimeter of the shaded rectangle:** $$P_{shaded} = 2(h + w) = 2(3 + 4) = 2 \times 7 = 14$$ 6. **Explain why the perimeter is not twice the smaller rectangle's perimeter:** If we doubled the perimeter, it would be $2 \times 10 = 20$ cm. However, the shaded rectangle shares the common side where the two smaller rectangles join, so that side is not counted twice. Hence, the perimeter increases but not doubles. **Final answers:** - a) The perimeter of the shaded rectangle is $14$ cm. - b) The perimeter is not twice because the joined side is internal and does not add to the outer boundary, so the total perimeter increases less than double.