Rama builds a frame for a square canvas that has an area of 196 square inches. What is the perimeter of the canvas?
The Correct Answer and Explanation is:
To find the perimeter of a square canvas with an area of 196 square inches, we start by using the formula for the area of a square: Area=side2\text{Area} = \text{side}^2Area=side2
Given that the area is 196 square inches: side2=196\text{side}^2 = 196side2=196
Now, take the square root of both sides: side=196=14 inches\text{side} = \sqrt{196} = 14 \text{ inches}side=196=14 inches
The perimeter of a square is the total length around the square, which is calculated by: Perimeter=4×side\text{Perimeter} = 4 \times \text{side}Perimeter=4×side Perimeter=4×14=56 inches\text{Perimeter} = 4 \times 14 = 56 \text{ inches}Perimeter=4×14=56 inches
✅ Correct Answer: 56 inches
📝 Explanation (300 words):
In geometry, a square is a four-sided polygon (a quadrilateral) where all four sides are equal in length and all angles are right angles. To solve this problem, we were given the area of a square canvas and asked to find its perimeter.
The area of a square is found using the formula: Area=side2\text{Area} = \text{side}^2Area=side2
That means you multiply one side by itself. In this case, the area is given as 196 square inches. To find the length of one side, we reverse the process by taking the square root of 196: 196=14\sqrt{196} = 14196=14
This tells us that each side of the square canvas is 14 inches long.
Next, we use the formula for the perimeter of a square: Perimeter=4×side\text{Perimeter} = 4 \times \text{side}Perimeter=4×side
Multiplying 4 by the side length (14 inches) gives: 4×14=564 \times 14 = 564×14=56
So, the perimeter of the canvas is 56 inches. This is the total distance around the square and represents the length of the frame Rama would need to enclose the canvas.
Understanding how to move between area and perimeter for a square is essential, especially in real-life applications like framing, construction, or fabric measurement. This problem is a practical example of applying basic geometry formulas to solve a real-world task.
