1. **Problem statement:** We have a triangular dog house with sides in the ratio 2:2:1, where the shortest side (base) is 1 meter. Inside, there is a smaller triangular storage area on top with a base of 25 cm (0.25 meters) parallel to the floor. We need to find the lengths of the two slanting sides of this smaller triangle, labeled $x$ and $y$. 2. **Understanding the problem:** The large triangle has sides in ratio 2:2:1, so the two equal sides are each $2$ times the shortest side. Since the shortest side is 1 meter, the two equal sides are each $2 \times 1 = 2$ meters. 3. **Key idea:** The smaller triangle on top is similar to the larger triangle because it shares the same angles and its base is parallel to the base of the larger triangle. 4. **Similarity ratio:** The base of the smaller triangle is 0.25 meters, and the base of the larger triangle is 1 meter. So the similarity ratio is $$r = \frac{0.25}{1} = 0.25.$$ 5. **Finding $x$ and $y$:** Since the triangles are similar, the sides scale by the same ratio $r$. The two equal sides of the larger triangle are 2 meters each, so the corresponding sides $x$ and $y$ of the smaller triangle are: $$x = y = 2 \times 0.25 = 0.5 \text{ meters}.$$ 6. **Final answer:** The lengths of the two sides of the storage area are $x = 0.5$ meters and $y = 0.5$ meters.