A rectangular photo frame X is of 90 cm length and 70 cm width and a square frame Y is of side 80 cm. Then which of the following is correct ?

Question

Accepted Answer

To determine why Option 4 is the correct answer, let's calculate the perimeter of both frames X and Y and analyze each option.

1. **Perimeter of Frame X:**
   - Frame X is a rectangle with a length of 90 cm and a width of 70 cm.
   - The formula for the perimeter of a rectangle is: 
     $$
     \text{Perimeter} = 2 \times (\text{Length} + \text{Width})
     $$
   - Substituting the given values:
     $$
     \text{Perimeter of X} = 2 \times (90 + 70) = 2 \times 160 = 320 \text{ cm}
     $$

2. **Perimeter of Frame Y:**
   - Frame Y is a square with a side length of 80 cm.
   - The formula for the perimeter of a square is:
     $$
     \text{Perimeter} = 4 \times \text{Side}
     $$
   - Substituting the given value:
     $$
     \text{Perimeter of Y} = 4 \times 80 = 320 \text{ cm}
     $$

Now, let's evaluate each option:

1. **Option 1: Perimeter of frame X is 6300 sq.cm**
   - This option incorrectly uses the unit "sq.cm," which is a unit of area, not perimeter. Additionally, the calculated perimeter of frame X is 320 cm, not 6300 sq.cm. Therefore, this option is incorrect.

2. **Option 2: Perimeter of frame Y is 6400 sq.cm**
   - Similar to Option 1, this option incorrectly uses "sq.cm" for perimeter. The calculated perimeter of frame Y is 320 cm, not 6400 sq.cm. Thus, this option is incorrect.

3. **Option 3: Perimeter of both X and Y frames is same and is equal to 320 sq.cm**
   - While it correctly states that the perimeters are the same, it incorrectly uses "sq.cm" instead of "cm." Perimeter is measured in linear units, not square units. Therefore, this option is incorrect.

4. **Option 4: Perimeter of both X and Y frames is equal to 320 cm**
   - This option correctly states that the perimeters of both frames X and Y are equal and correctly uses the unit "cm." The calculated perimeter for both frames is indeed 320 cm. Therefore, this option is correct.

In conclusion, Option 4 is the correct answer because it accurately describes the perimeters of both frames X and Y as being equal to 320 cm, using the correct unit of measurement.