"Which special version of the Pythagorean Theorem can you use to find the
length of any square's diagonal, d, using only the length of its side, s?"
I have no idea what this means, I saw a question like this in another question but didn't quite understand please help!
And please don't rat me out if you somehow find out who I am to my school-
They'll friggin kick me out-
Thanks!
the square's diagonal is the hypotenuse of an isosceles right triangle
... the two perpendicular sides are the same length
s^2 + s^2 = h^2 ... 2 s^2 = h^2 ... s√2 = h
find the diagonal by multiplying the side by √2
No worries! I'm here to help you understand. There is a special version of the Pythagorean Theorem that specifically applies to squares. To find the length of any square's diagonal (d) using only the length of its side (s), you can use the formula:
d = s * √2
Here's an explanation of how we derive this formula using 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 the case of a square, all sides are congruent, meaning they have the same length. Let's call this length s. Now, if we draw a right triangle within the square, with one side along the diagonal and the other two sides along the sides of the square, we have a right triangle where the lengths of the two shorter sides are s.
According to the Pythagorean Theorem, we can write the equation:
s^2 + s^2 = d^2
Simplifying this equation, we get:
2s^2 = d^2
Now, to solve for d, we take the square root of both sides:
√(2s^2) = √(d^2)
√(2)s = d
Therefore, the length of the diagonal (d) of any square is equal to the length of its side (s) multiplied by the square root of 2 (√2).
To find the length of a square's diagonal, you can simply multiply the length of the side by the square root of 2. No other information is required.