The ratio of the length and breadth of a rectangular table cover is 2:5. If the perimeter of the sheet is 140 cm, find its dimensions.

Answer

To solve the problem step by step, we will follow the given information and use algebra to find the dimensions of the rectangular table cover.

### Step 1: Understand the Ratio
The ratio of the length (l) to the breadth (b) of the table cover is given as 2:5. This can be expressed as:
\[ \frac{l}{b} = \frac{2}{5} \]

### Step 2: Express Length in Terms of Breadth
From the ratio, we can cross-multiply to express the length in terms of breadth:
\[ 5l = 2b \]
This can be rewritten as:
\[ l = \frac{2}{5}b \]
Let’s call this **Equation 1**.

### Step 3: Use the Perimeter Formula
The perimeter (P) of a rectangle is given by the formula:
\[ P = 2(l + b) \]
According to the problem, the perimeter is 140 cm:
\[ 140 = 2(l + b) \]

### Step 4: Simplify the Perimeter Equation
Dividing both sides of the equation by 2 gives:
\[ l + b = 70 \]
Let’s call this **Equation 2**.

### Step 5: Substitute Equation 1 into Equation 2
Now we will substitute the expression for l from Equation 1 into Equation 2:
\[ \frac{2}{5}b + b = 70 \]

### Step 6: Combine Like Terms
To combine the terms, we can express b as a fraction:
\[ \frac{2}{5}b + \frac{5}{5}b = 70 \]
This simplifies to:
\[ \frac{7}{5}b = 70 \]

### Step 7: Solve for Breadth (b)
To find b, multiply both sides by 5:
\[ 7b = 350 \]
Now, divide by 7:
\[ b = 50 \text{ cm} \]

### Step 8: Find Length (l)
Now that we have the value of breadth, we can find the length using Equation 1:
\[ l = \frac{2}{5}b = \frac{2}{5} \times 50 = 20 \text{ cm} \]

### Conclusion
The dimensions of the rectangular table cover are:
- Length (l) = 20 cm
- Breadth (b) = 50 cm