1. **Problem Statement:** You are given a rectangular "L" shape at scale 1:1 and asked to enlarge it successively by scales 2:1, 3:1, and 4:1. 2. **Understanding Enlargement:** Enlargement means multiplying all linear dimensions of the shape by the scale factor. 3. **Formula for Enlargement:** If the original length is $L$, then the enlarged length at scale $k:1$ is: $$L_{new} = k \times L$$ 4. **Applying the scales:** - At scale 1:1, the shape remains the same size: $L_{1} = 1 \times L = L$ - At scale 2:1, the shape doubles in size: $L_{2} = 2 \times L$ - At scale 3:1, the shape triples in size: $L_{3} = 3 \times L$ - At scale 4:1, the shape quadruples in size: $L_{4} = 4 \times L$ 5. **Explanation:** Each enlargement multiplies every length of the original "L" shape by the scale factor, making the shape proportionally larger while keeping the same shape. 6. **Summary:** The successive enlarged shapes have lengths $L$, $2L$, $3L$, and $4L$ respectively, corresponding to scales 1:1, 2:1, 3:1, and 4:1.