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?
My answer: A special version of the Pythagorean Theorem I can use to find the length of any square's diagonal using only the length of its side is by using s² + s² = d²
d^2 = s^2 + s^2
The basic equation is
d^2 = base squared plus height squared
I learned it as
a^2 + b^2 = c^2
Hope this helps :)
Agree
Actually, the correct special version of the Pythagorean Theorem to find the length of any square's diagonal, d, using only the length of its side, s, is:
d = s√2
This formula is derived from the Pythagorean Theorem, where the squares of the two sides of a right triangle are equal to the square of the hypotenuse. In the case of a square, all sides are equal, so if we consider one side as the base of the right triangle and the diagonal as the hypotenuse, using the Pythagorean Theorem gives us:
s² + s² = d²
2s² = d²
Taking the square root of both sides gives:
√(2s²) = √(d²)
s√2 = d
So, the correct special version of the Pythagorean Theorem to find the length of any square's diagonal using only the length of its side is d = s√2.
That's correct! The special version of the Pythagorean Theorem you referred to is used specifically for finding the length of the diagonal (d) of a square using only the length of its side (s).
To understand why this version works, let's break it down:
1. Start with a square, where all four sides are equal in length.
2. Label one side of the square as s, which represents the length of that side.
3. Since the square has four equal sides, we can label the other three sides as s as well.
4. Using the regular Pythagorean Theorem formula (a² + b² = c²), we can apply it to one of the right triangles inside the square.
5. In this case, we can consider one side of the square as the base of the right triangle (s), another side as the height (s), and the diagonal as the hypotenuse (d).
6. So, using the Pythagorean Theorem, we have (s)² + (s)² = (d)².
7. Simplifying this equation, we get s² + s² = d².
Therefore, the equation s² + s² = d² allows us to calculate the length of the diagonal (d) of any square when we only know the length of its side (s).