Rama builds a frame for a square canvas that has an area of 196 square inches. What is the perimeter of the canvas?

Understand the Problem

The question is asking for the perimeter of a square canvas given its area of 196 square inches. To solve this, we need to first find the length of one side of the square by taking the square root of the area, and then use that length to calculate the perimeter.

Answer

The perimeter of the canvas is $56$ inches.

Steps to Solve

Calculate the Side Length from the Area

To find the side length of the square, take the square root of the area.

$$ \text{Side length} = \sqrt{\text{Area}} = \sqrt{196} $$

Evaluate the Square Root

Calculate the value of the square root.

$$ \sqrt{196} = 14 $$

Thus, the side length is 14 inches.

Calculate the Perimeter

The perimeter ( P ) of a square can be calculated using the formula:

$$ P = 4 \times \text{Side length} $$

Substitute the Side Length into the Perimeter Formula

Now substitute the side length into the perimeter formula:

$$ P = 4 \times 14 $$

Calculate the Final Perimeter

Now carry out the multiplication:

$$ P = 56 $$

So, the perimeter of the canvas is 56 inches.

The perimeter of the canvas is $56$ inches.

More Information

The perimeter of a square is always four times the length of one side. By understanding the relationship between area and side length, we can easily find the perimeter when given the area.

Tips

Forgetting to take the square root: Some may incorrectly use the area as a side length without taking the square root first.
Incorrect calculation: Always double-check calculations for square roots and multiplication to avoid errors.

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