find the length of a side of a square whose diagonal is 16 in.
45, 45, 90 triangle
s sqrt 2 =16
s = 16/sqrt 2
= 11.31
To find the length of a side of a square given its diagonal, we can use the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In this case, the diagonal of the square is the hypotenuse, and the two sides are the lengths of the square's sides.
Let's assume that the length of a side of the square is "x". Then we can set up the following equation using the Pythagorean theorem:
x^2 + x^2 = 16^2
Simplifying the equation:
2x^2 = 16^2
Dividing both sides by 2:
x^2 = 16^2 / 2
Taking the square root of both sides to solve for x:
x = √(16^2 / 2)
Calculating the value:
x = √(256 / 2) = √128 ≈ 11.31
Therefore, the length of a side of the square is approximately 11.31 inches.