Find an expression for the area of a square with the given perimeter.
1. P= (12x+20y) in.
2. P= (36a-16b) cm.
In a square the perimeter would be 4 times the length of a side,
so divide 12x + 20y by 4 to get 3x+5y as the length of the side
Then the area of the first one would be
(3x+5y)(3x+5y) or (3x+5y)^2
do the second one the same way
To find the expression for the area of a square with a given perimeter, we need to divide the perimeter by 4 and then square the result.
Using the given information:
1. P = (12x + 20y) in.
The side length of the square is represented by (12x + 20y)/4, and squaring that result will give us the area.
So, the expression for the area of the square is:
A = ((12x + 20y)/4)^2 square inches.
2. P = (36a - 16b) cm.
The side length of the square is represented by (36a - 16b)/4, and squaring that result will give us the area.
So, the expression for the area of the square is:
A = ((36a - 16b)/4)^2 square centimeters.
To find the expression for the area of a square with a given perimeter, we can use the formula:
Area = (Perimeter/4)^2
Let's solve the two given examples to find their respective expressions:
1. P = (12x + 20y) in.
To find the expression for the area, we substitute the given perimeter (P) into the formula:
Area = ((12x + 20y)/4)^2
Simplifying further:
Area = (3x + 5y)^2
So, the expression for the area of a square with perimeter (12x + 20y) inches is (3x + 5y)^2.
2. P = (36a - 16b) cm.
Using the same formula, we substitute the given perimeter (P) into the formula:
Area = ((36a - 16b)/4)^2
Simplifying further:
Area = (9a - 4b)^2
Thus, the expression for the area of a square with perimeter (36a - 16b) centimeters is (9a - 4b)^2.