The area of a square and a rectangle are equal. If side of the square is 40 cm and breadth of the rectangle is 25cm, find the length of the rectangle

Question

Accepted Answer

To determine the length of the rectangle, we start by understanding that the area of the square is equal to the area of the rectangle. Given that the side of the square is 40 cm, we can calculate the area of the square as follows:

$$ \text{Area of the square} = \text{side} \times \text{side} = 40 \, \text{cm} \times 40 \, \text{cm} = 1600 \, \text{cm}^2 $$

Since the area of the square is equal to the area of the rectangle, the area of the rectangle is also 1600 cm². The formula for the area of a rectangle is:

$$ \text{Area of the rectangle} = \text{length} \times \text{breadth} $$

We know the breadth of the rectangle is 25 cm, so we can set up the equation:

$$ \text{length} \times 25 \, \text{cm} = 1600 \, \text{cm}^2 $$

To find the length, we solve for it by dividing both sides of the equation by 25 cm:

$$ \text{length} = \frac{1600 \, \text{cm}^2}{25 \, \text{cm}} = 64 \, \text{cm} $$

Thus, the length of the rectangle is 64 cm, which corresponds to Option 3.

Now, let's explain why the other options are incorrect:

1. **Option 1: 81 cm** - If the length were 81 cm, the area of the rectangle would be $ 81 \, \text{cm} \times 25 \, \text{cm} = 2025 \, \text{cm}^2 $, which is greater than 1600 cm². Therefore, this option is incorrect.

2. **Option 2: 65 cm** - If the length were 65 cm, the area of the rectangle would be $ 65 \, \text{cm} \times 25 \, \text{cm} = 1625 \, \text{cm}^2 $, which is also greater than 1600 cm². Thus, this option is incorrect.

3. **Option 4: 74 cm** - If the length were 74 cm, the area of the rectangle would be $ 74 \, \text{cm} \times 25 \, \text{cm} = 1850 \, \text{cm}^2 $, which is again greater than 1600 cm². Therefore, this option is incorrect.

In conclusion, the only option that satisfies the condition of the areas being equal is Option 3, with a length of 64 cm.