Proof for the equations are given below.
Step-by-step explanation:
- Step 1: The diagram is made up of 1 square and 4 rectangles, and the whole figure is a square. So the area of the larger square (figure) must be equal to the sum of the areas of the 4 rectangles and 1 square. Find the area of the figure or the larger square.
Area of a square = (side length)²
Here, the length of the side of the larger square = a + b
⇒ Area of the square = (a + b)²
- Step 2: Find the sum of the areas of the 1 square and 4 rectangles.
Here, the side of the square = a - b
⇒ Area of the square (in the center) = (a - b)²
Area of a rectangle = length × width
Here, length = a and width = b
⇒ Area of the 4 rectangles = 4 × a × b = 4ab
∴ Sum of the areas = (a - b)² + 4ab
Now, both these areas are the same.
⇒ (a - b)² + 4ab = (a + b)²
- Step 3: Expand the above equation.
Left Hand Side = (a - b)² + 4ab = a² - 2ab + b² + 4ab = a² + 2ab + b²
= (a + b)²
= Right Hand Side of the equation
Mean = Numbers added up and divided by the amount of numbers.
Mean = 45 + 90 + 18 + 53 + 13 + 38 + 22 + 59 + 49
Mean = 387 ÷ 9
Mean = 43
Median = The middle number when arranged in order
Median = 13, 18, 22, 38, 45, 49, 53, 59, 90
Median = 45
Mode = The number that occurs most often
Mode = There is no mode because each number occurs the same amount of times
Range = Biggest number takeaway smallest number
Range = 90 - 13
Range = 77
If the pi = 3.14
then the answer is ≈5.42
we are going to times the both sides by two
