Find the perimeter of a square if the diagonal measurement is 36 inches.
45 45 90 triangle --> 1,1,sqrt 2
side * sqrt 2 = 36
side = 36/sqrt 2
4 sides = 4*36 /sqrt 2
= 144 (sqrt 2/ 2)
= 72 sqrt 2
To calculate the perimeter of a square, we need to determine the length of one side.
In this case, we are given the diagonal measurement, which is the line connecting opposite corners of the square. We can use the Pythagorean theorem to find the length of one side.
The Pythagorean theorem states that in any right triangle, the square of the length of the hypotenuse (the diagonal) is equal to the sum of the squares of the other two sides. In this case, two sides of the right triangle are the length of one side of the square, so we'll call it "s", and the hypotenuse is the diagonal, which is given as 36 inches.
The Pythagorean theorem equation can be written as:
s^2 + s^2 = 36^2
Simplifying the equation, we have:
2s^2 = 36^2
Dividing both sides by 2, we get:
s^2 = 36^2 / 2
Taking the square root of both sides, we find:
s = √(36^2 / 2)
Now, let's calculate s:
s = √(1296 / 2)
s = √648
s = 24
Therefore, the length of one side of the square is 24 inches.
To find the perimeter, we need to multiply the length of one side by 4 (since a square has four equal sides).
Perimeter = 4 * s
Perimeter = 4 * 24
Perimeter = 96
Hence, the perimeter of the square is 96 inches.