If the difference between the perimeter of a square field A and its side is 48 cm. Side of square field B is 4 cm less than the side of square field A. Then, find the area of square field B.
144 cm2
Understanding the Square Fields
We are given information about two square fields, let's call them Field A and Field B. We need to find the area of Field B.
Calculating the Side of Field A
Let the side length of square Field A be represented by the variable '$a$'.
The perimeter of a square is calculated by the formula: Perimeter = 4 × side.
So, the perimeter of Field A is $4a$ cm.
The problem states that the difference between the perimeter of Field A and its side is 48 cm.
We can write this as an equation:
Perimeter of A - Side of A = 48
Substituting the formula for the perimeter:
$$4a - a = 48$$
Now, we simplify the equation:
$$3a = 48$$
To find the side '$a$', we divide both sides by 3:
$$a = \frac{48}{3}$$
$$a = 16$$
Therefore, the side length of square Field A is 16 cm.
Calculating the Side of Field B
The problem states that the side of square Field B is 4 cm less than the side of square Field A.
Let the side length of square Field B be represented by the variable '$b$'.
Using the side length of Field A ($a = 16$ cm), we can find '$b$':
$$b = a - 4$$
$$b = 16 - 4$$
$$b = 12$$
So, the side length of square Field B is 12 cm.
Calculating the Area of Field B
The area of a square is calculated by the formula: Area = side × side or Area = side$^2$.
We need to find the area of square Field B, which has a side length '$b$' of 12 cm.
Area of Field B = $b^2$
Area of Field B = $12^2$
Area of Field B = $12 \times 12$
Area of Field B = 144
The area is measured in square centimeters (cm$^2$).
Thus, the area of square Field B is 144 cm$^2$.
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