Find the perimeter and area of a square with diagonal length of 20cm.. Leave your answer in simplest radical form
let the side be x
x^2 + x^2 = 20^2
solve for x, once you have that
A = x^2
P + 4x
a=5,b=12,c=?
To find the perimeter and area of a square with diagonal length of 20 cm, we need to start by finding the side length of the square.
Since the diagonal of a square divides it into two congruent right triangles, we can use the Pythagorean theorem to find the side length.
Let's denote the side length of the square as "s".
Using the Pythagorean theorem, we have:
s^2 + s^2 = 20^2
2s^2 = 400
s^2 = 200
Taking the square root of both sides, we get:
s = √200 = 10√2 cm
Now that we know the side length, we can find the perimeter and area of the square.
Perimeter of the square = 4 * side length
= 4 * (10√2) cm
= 40√2 cm
Area of the square = side length^2
= (10√2)^2
= 100 * 2
= 200 cm^2
Therefore, the perimeter of the square is 40√2 cm and the area is 200 cm^2.
To find the perimeter and area of a square with a diagonal length of 20 cm, we can use the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the sum of the squares of the lengths of the two shorter sides is equal to the square of the length of the hypotenuse (the longest side).
In a square, the diagonals are also the hypotenuses of the right triangles formed by the sides of the square. The sides of the square are congruent, so we can use the Pythagorean theorem to find the length of one side.
Let's denote the length of one side of the square as "s". Then, by the Pythagorean theorem:
s^2 + s^2 = (20 cm)^2
2s^2 = 400 cm^2
Dividing both sides by 2, we get:
s^2 = 200 cm^2
Taking the square root of both sides, we get:
s = √200 cm
Now, we can find the perimeter and area of the square using the side length we just calculated.
Perimeter of a square = 4s
Perimeter = 4(√200 cm) = 4√200 cm
Area of a square = s^2
Area = (√200 cm)^2 = 200 cm^2
Therefore, the perimeter of the square is 4√200 cm and the area is 200 cm^2.