I have some questions I have to answer can I get a formula for to find the diagonal length of any paper square? (it’s a project.)
if the side lengths of a rectangle are a and b
then A = a * b
If it is really a square then b = a
then
A = a^2
and
d^2 = a^2 + b^2
so
d = sqrt (a^2+ b^2)
and
if really square b = a
and
d = a sqrt 2
You are welcome.
Certainly! To find the diagonal length of a square piece of paper, you can use the Pythagorean theorem. The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In the case of a square piece of paper, the diagonal forms the hypotenuse, and the sides of the square are the other two sides. Since all sides of a square are equal in length, you can denote the length of each side as "s."
Using the Pythagorean theorem, the formula to find the diagonal length of a square becomes:
Diagonal length = square root of (s^2 + s^2)
Simplifying this, you get:
Diagonal length = square root of (2s^2)
So, to find the diagonal length of any paper square, you can use the formula:
Diagonal length = square root of (2 * side length squared)
This formula will work for any size of square paper. Just substitute the value of the side length (s) into the formula, and calculate the square root of the result to find the diagonal length.