When building a house, the architect in charge wants the proportion between the dimensions of the dining room, the living room and the bedroom to be 5:7:4. If the length and width of the dining room are 7 and 5 meters, respectively, what are the dimensions of the other rooms?

Given:
- Ratio of dining room (5), living room (7), and bedroom (4).
- Dimensions of dining room: length = 7 meters, width = 5 meters.

Calculate the total ratio sum:

5 + 7 + 4 = 16

Find the area of the dining room:

\text{Area of dining room} = 7 \times 5 = 35 \text{ square meters}

Calculate the scale factor:

\text{Scale factor} = \frac{35}{5} = 7

Find dimensions of the living room:

\text{Area of living room} = 7 \times 7 = 49 \text{ square meters}
\text{Length of living room} = 1.4 \times 7 = 9.8 \text{ meters}
\text{Width of living room} = 1 \times 7 \text{ meters}

Find dimensions of the bedroom:

\text{Area of bedroom} = 4 \times 7 = 28 \text{ square meters}
\text{Length of bedroom} = 1.4 \times 4 = 5.6 \text{ meters}
\text{Width of bedroom} = 1 \times 4 \text{ meters}

Answer:

\text{Dimensions of the living room: (9.8 meters, 7 meters)}
\text{Dimensions of the bedroom: (5.6 meters, 4 meters)}