A composite figure is formed by combining a square and a triangle. Its total area is 32.5 feet squared. The area of the triangle is 7.5 ft squared. What is the length of each side of the square? Explain.
THANK YOU!!
area of square = 32.5-7.5 = 25
so it is 5 by 5 = 25
like s = 5
To determine the length of each side of the square, we need to first find the area of the square.
Let's assume that the length of each side of the square is "x" feet.
The area of a square is given by the formula A = side^2, where A represents the area and side represents the length of each side.
So, the area of the square is x^2 square feet.
The total area of the composite figure is given as 32.5 square feet. This area is formed by combining the square and the triangle.
The area of the triangle is given as 7.5 square feet.
To find the area of the composite figure, we add the areas of the square and the triangle:
x^2 + 7.5 = 32.5
To solve for x, we subtract 7.5 from both sides of the equation:
x^2 = 32.5 - 7.5
x^2 = 25
Now, we can take the square root of both sides to find the value of x:
√x^2 = √25
x = 5
Therefore, each side of the square is 5 feet long.
To find the length of each side of the square in the composite figure, we can use the information given about the total area and the area of the triangle.
Let's assume that the side length of the square is "x" feet.
The area of a square is given by the formula: Area = side length squared. So the area of the square would be x^2 square feet.
The area of the triangle is given as 7.5 ft^2.
To find the remaining area of the composite figure, we need to subtract the area of the triangle from the total area:
Remaining area = Total area - Area of the triangle
Remaining area = 32.5 ft^2 - 7.5 ft^2
Remaining area = 25 ft^2
Since the composite figure is made up of a square and a triangle, the remaining area must belong to the square.
Therefore, we can set up the equation:
x^2 = 25 ft^2
To solve for x (the side length of the square), we need to take the square root of both sides of the equation:
√(x^2) = √(25 ft^2)
x = √25 ft
x = 5 ft
So, the length of each side of the square in the composite figure is 5 feet.