the perimeter of two square are 848cm and 436cm find the perimeter of square whose area is equal to the sum of areas of two square.
each side of first one is 848/4 or 212 cm
each side of the 2nd is 436/4 or 109 cm
so the area of the first = 212^2 cm^2 = 44944 cm^2
the area of the 2nd is 109^2 cm = 11881 cm^2
total area = 56825 cm^2
each side is √56825 = 5√2273
and the perimeter = 20√2273
= appr 953.52
To solve this problem, we need to follow a few steps:
Step 1: Find the lengths of the sides of the two squares
We know that the perimeter of a square is equal to 4 times the length of one side. Let's call the side lengths of the first and second square "a" and "b", respectively.
From the given information, we can set up two equations:
4a = 848 (Equation 1)
4b = 436 (Equation 2)
Solving these equations will give us the values of "a" and "b".
Step 2: Find the areas of the two squares
The area of a square is calculated by multiplying the length of one side by itself. The formulas for the area of each square are:
Area of the first square = a^2
Area of the second square = b^2
Step 3: Find the sum of the areas of the two squares
Add the areas of the first and second squares together to find the total area:
Total area = Area of the first square + Area of the second square
Step 4: Find the side length of the square with the equal area
To find the side length of the square with an area equal to the sum of the areas of the two squares, we need to calculate the square root of the total area:
Side length of the square with equal area = √(Total area)
Step 5: Find the perimeter of the square with equal area
Finally, calculate the perimeter of the square using the formula:
Perimeter = 4 * (Side length of the square with equal area)
By following these steps, you will be able to find the perimeter of the square whose area is equal to the sum of the areas of the two squares.