the perimeter of two squares are 848cm and436cm. find the perimeter of a square whose area is equal to thesum of the areas of two squares
To find the perimeter of a square whose area is equal to the sum of the areas of two squares, let's start by finding the side lengths of the two given squares.
Square 1:
Perimeter = 848 cm
Let's assume the side length of Square 1 is "a".
Perimeter of Square 1 = 4 * a = 848 cm
Solving for "a", we get:
a = 848 cm / 4 = 212 cm
Square 2:
Perimeter = 436 cm
Let's assume the side length of Square 2 is "b".
Perimeter of Square 2 = 4 * b = 436 cm
Solving for "b", we get:
b = 436 cm / 4 = 109 cm
Now, let's find the area of each square.
Area of Square 1 = a^2 = 212 cm * 212 cm = 44944 cm^2
Area of Square 2 = b^2 = 109 cm * 109 cm = 11881 cm^2
The sum of the areas of the two squares = Area of Square 1 + Area of Square 2 = 44944 cm^2 + 11881 cm^2 = 56825 cm^2
To find the side length of the square whose area is equal to the sum of the areas of the two squares, we take the square root of the sum of the areas:
Side length of new square = √(56825 cm^2) ≈ 238.6 cm
Finally, we can find the perimeter of the new square by multiplying the side length by 4:
Perimeter of new square = 4 * 238.6 cm = 954.4 cm
Therefore, the perimeter of the new square whose area is equal to the sum of the areas of two squares is approximately 954.4 cm.
To solve this problem, we need to find the side length of the two squares, calculate their areas, and then find the side length of the new square. Finally, we can determine the perimeter of the new square. Here's how you can do it step by step:
Step 1: Find the side length of the first square:
If the perimeter of the first square is 848cm, divide it by 4 because each side of a square is equal.
Side length of the first square = 848cm / 4 = 212cm
Step 2: Find the side length of the second square:
If the perimeter of the second square is 436cm, divide it by 4 to get the side length.
Side length of the second square = 436cm / 4 = 109cm
Step 3: Find the areas of the two squares:
The area of a square is calculated by multiplying the side length by itself.
Area of the first square = (Side length of the first square)^2 = 212cm * 212cm
Area of the second square = (Side length of the second square)^2 = 109cm * 109cm
Step 4: Find the sum of the areas of the two squares:
Sum of the areas = Area of the first square + Area of the second square
Step 5: Find the side length of the new square:
Since the area of a square is equal to the sum of the areas of the two squares, we can find the side length of the new square by taking the square root of the sum of the areas.
Side length of the new square = √(Sum of the areas)
Step 6: Calculate the perimeter of the new square:
Perimeter of a square is calculated by multiplying the side length by 4.
Perimeter of the new square = Side length of the new square * 4
By following these steps, you can find the perimeter of the square whose area is equal to the sum of the areas of the two squares.