a square has a diagonal measurement of 8 radical 2 inches. calculate its perimeter.
A 45-45-90 deg triangle is one-half a square.
The length of a leg opposite a 45 deg angle equals one-half the length of the hypotenuse times the square root of 2.
to find one of the sides of the square,
c = a * sqrt2 (the diagonal)
8(sqrt2) = a * sqrt2
a = 8
P = 4s
P = 4 * 8
P = 32
To find the perimeter of a square, we need to know the length of one side. However, we are given the diagonal measurement of the square.
We can apply the Pythagorean theorem to relate the diagonal and the sides of the square. According to the Pythagorean theorem, in a right triangle, the square of the hypotenuse (the diagonal) is equal to the sum of the squares of the other two sides.
Let's denote the length of one side of the square as "s". We can form a right triangle by drawing a diagonal from one corner of the square to the opposite corner.
Using the Pythagorean theorem, we have:
(diagonal)^2 = (side)^2 + (side)^2
(8√2)^2 = s^2 + s^2
128 = 2s^2
Dividing both sides by 2, we get:
64 = s^2
Taking the square root of both sides, we find:
√64 = √(s^2)
8 = s
So, we have determined that the length of one side of the square is 8 inches.
The perimeter of a square is found by multiplying the length of one side by 4. Since we know the length of one side is 8 inches, the perimeter of the square is:
Perimeter = 4 * side
Perimeter = 4 * 8
Perimeter = 32 inches
Therefore, the perimeter of the given square is 32 inches.