A drawing room is 7.5 m long 6.5 m broad and 6 m high . Find the length of paper 2.5 dm wide to cover its walls allowing 8 sq. m for doors :

Options

A. a. 368 m
B. b. 640 m
C. c. 625 m
D. d. 888 m

Answer

To solve the problem of finding the length of paper needed to cover the walls of a drawing room, we will follow these steps:

### Step 1: Calculate the Area of the Walls
The drawing room has dimensions:
- Length (l) = 7.5 m
- Width (w) = 6.5 m
- Height (h) = 6 m

The total area of the walls can be calculated using the formula:
\[ \text{Area of walls} = 2 \times (l + w) \times h \]

Substituting the values:
\[ \text{Area of walls} = 2 \times (7.5 + 6.5) \times 6 \]
\[ = 2 \times 14 \times 6 \]
\[ = 168 \, \text{m}^2 \]

### Step 2: Subtract the Area for Doors
We need to allow for the area taken up by doors, which is given as 8 m². Therefore, the actual area to be covered is:
\[ \text{Actual area} = \text{Area of walls} - \text{Area of doors} \]
\[ = 168 - 8 \]
\[ = 160 \, \text{m}^2 \]

### Step 3: Convert the Area to dm²
Since the width of the paper is given in decimeters (dm), we need to convert the area from m² to dm².
1 m² = 100 dm², so:
\[ \text{Actual area in dm}^2 = 160 \times 100 = 16000 \, \text{dm}^2 \]

### Step 4: Calculate the Length of the Paper
The width of the paper is given as 2.5 dm. To find the length of the paper required, we can use the formula:
\[ \text{Length} = \frac{\text{Area}}{\text{Width}} \]
Substituting the values:
\[ \text{Length} = \frac{16000}{2.5} \]
\[ = 6400 \, \text{dm} \]

### Step 5: Convert Length to Meters
To convert the length from dm to meters, we divide by 10 (since 1 m = 10 dm):
\[ \text{Length in meters} = \frac{6400}{10} = 640 \, \text{m} \]

### Final Answer
The length of paper required to cover the walls of the drawing room is **640 meters**.

---