1. **Problem statement:** We have a large square with side length $4.472$ units and a smaller blue shaded square inside it with side length $2.236$ units. There is a third length unknown. We need to find: a) The third length. b) The area of the large square. c) The area of the blue shaded square. d) The fraction of the blue shaded area relative to the total area. 2. **Given lengths:** - Length 1: $2.236$ units - Length 2: $4.472$ units - Length 3: Unknown 3. **Step a) Find the third length:** Notice that $4.472$ is approximately twice $2.236$ since $2.236 \times 2 = 4.472$. The third length is the difference between the large side and the smaller side: $$\text{Third length} = 4.472 - 2.236 = 2.236$$ So the third length is also $2.236$ units. 4. **Step b) Area of the large square:** The area of a square is side squared: $$A_{large} = (4.472)^2$$ Calculate: $$A_{large} = 4.472 \times 4.472 = 20.000784 \approx 20$$ 5. **Step c) Area of the blue shaded square:** Side length is $2.236$ units, so: $$A_{blue} = (2.236)^2$$ Calculate: $$A_{blue} = 2.236 \times 2.236 = 5.000896 \approx 5$$ 6. **Step d) Fraction of blue area to total area:** $$\text{Fraction} = \frac{A_{blue}}{A_{large}} = \frac{5}{20} = \frac{1}{4} = 0.25$$ **Final answers:** - Third length: $2.236$ units - Area of large square: $20$ square units - Area of blue square: $5$ square units - Fraction of blue area: $\frac{1}{4}$ or $0.25$