If the diagonal of a square has a length of 10 suare root of 2 cm, find the area of the square and the perimeter of the square.
Diagonal forms right triangle, with sides of square as two of the sides. Use Pythagorean theorem.
a^2 + b^2 = (10√2)^2
However, since a = b,
2a^2 = (10√2)^2
Perimeter = 4a
I'll leave the calculations for you.
50
To find the area and perimeter of a square, we need to know the length of one side. In this case, we are given the length of the diagonal, which we can use to calculate the side length using the Pythagorean theorem.
Let's consider the diagonal of the square as the hypotenuse of a right triangle formed by two sides of the square. The formula for the Pythagorean theorem is:
a^2 + b^2 = c^2
Where:
a and b are the lengths of the two sides of the right triangle
c is the length of the hypotenuse (diagonal of the square)
Since all sides of a square are equal, we can assume that both sides of the right triangle have the same length, which is also equal to the side length of the square. Let's call it "s".
Applying the Pythagorean theorem, we have:
s^2 + s^2 = (10√2)^2
Simplifying the equation:
2s^2 = 200
Divide both sides by 2:
s^2 = 100
Taking the square root of both sides, we find the length of one side of the square:
s = √100
s = 10 cm
Now that we have the side length of the square, we can calculate the area and the perimeter.
Area of a square = side length^2
Perimeter of a square = 4 * side length
Plugging in the value of the side length:
Area = 10 cm * 10 cm = 100 cm^2
Perimeter = 4 * 10 cm = 40 cm
So, the area of the square is 100 square centimeters and the perimeter is 40 centimeters.