2. 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?
a^2 + s^2 = b^2 usual version for hypotenuse(diagonal) of rectangle d given sides a and b
but if a = b = s
then
s^2+s^2 = d^2
so
2 s^2 = d^2
d = s sqrt 2
Ah, the special version of the Pythagorean Theorem for squares! Well, you know what they say – "When in doubt, bring out the clowns!" Just kidding. Let's dive into the answer with a little clownish twist!
To find the length of a square's diagonal, you can use the "Pythagorean Theorem's Square Dance Remix." It goes a little something like this:
d² = s² + s²
Or, to put it in human terms, the length of that clownish diagonal squared (d²) is equal to the length of one side squared (s²) plus the length of another side squared (s²).
After all the dancing around, you can just take the square root of both sides to find the elusive length of that square's diagonal. And there you have it, my silly friend – the magical formula to unlock the secret of a square's diagonal length!
The special version of the Pythagorean Theorem that can be used to find the length of a square's diagonal, given the length of its side, is as follows:
d = s√2
where:
d represents the length of the diagonal
s represents the length of the side of the square.
The special version of the Pythagorean Theorem that can be used to find the length of any square's diagonal is as follows:
d^2 = s^2 + s^2
To understand why this formula works, let's break it down step by step:
1. Start with a square with sides of length s.
2. Draw two perpendicular lines from opposite corners to create a right triangle inside the square.
3. The diagonal, d, of the square forms the hypotenuse of this right triangle.
4. By the Pythagorean Theorem, in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
5. In this case, both of the other two sides of the right triangle are equal to the length of a side of the square, s.
6. Therefore, we can represent this equation as d^2 = s^2 + s^2.
By finding the square root of both sides of the equation, we can solve for the length of the diagonal, d:
d = √(s^2 + s^2) or d = √2s^2
So, to find the length of any square's diagonal using only the length of its side, you can use the special version of the Pythagorean Theorem, which states that the square of the diagonal is equal to the sum of the squares of the two sides (both equal to the length of the side of the square).