Which special version of the Pythagorean Theorem can you use to find the length of any squares diagonal, d, using only the length of its side, 12 inches.
Please help been struggling with this for a long time
I can not imagine why you would need a "special" version. The plain vanilla version says that if the side of the square is length s then the length of a diagonal d is the hypotenuse of a right triangle with equal sides s.
d^2 = s^2 + s^2 = 2 s^2
so
d = s * sqrt (2)
or d is approximately 1.414 .... * s
To find the length of a square's diagonal using only the length of its side, we can use a special version of the Pythagorean theorem.
The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In the case of a square, all four sides are equal in length, so we can consider it as a right-angled isosceles triangle.
Let's say the length of the side of the square is 's', and the length of the diagonal (the hypotenuse) is 'd'.
Using the Pythagorean theorem, we have:
s^2 + s^2 = d^2
Simplifying this equation, we get:
2s^2 = d^2
To find the length of the diagonal, we can substitute the given length of the side ('12 inches') into the equation:
2(12^2) = d^2
2(144) = d^2
288 = d^2
Taking the square root of both sides to isolate 'd', we get:
d = √288
Now, we can calculate the value of 'd' using a calculator:
d ≈ 16.97 inches
Therefore, the length of the diagonal of the square with a side length of 12 inches is approximately 16.97 inches.