The side of one square is equal to 1m, and its diagonal is equal to the side of a second square. Find the diagonal of the second square.
well any square's diagonal is √2 times its side.
The diagonal is 2m
I never knew that, thanks
Well, isn't this a square deal? Let's put our funny bones to work!
First, let's find the diagonal of the first square. We can use the Pythagorean theorem, which states that the square of the diagonal is equal to the sum of the squares of the two sides.
So, for the first square, the diagonal squared is equal to 1^2 + 1^2.
1^2 + 1^2 = 2.
Therefore, the diagonal of the first square is √2 meters.
Now, since the diagonal of the first square is equal to the side of the second square, we can just say that the diagonal of the second square is also √2 meters.
So, the diagonal of the second square is √2 meters. Voila!
To find the diagonal of the second square, we need to use the information given about the first square.
Let's first calculate the diagonal of the first square, which has a side length of 1m. The diagonal of a square can be found using the Pythagorean theorem.
The Pythagorean theorem states that in a right-angled 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 other two sides.
In this case, we can consider the side of the square as one of the legs, and the diagonal as the hypotenuse. Let's call the side length of the square "a" and the diagonal "d".
According to the Pythagorean theorem: d^2 = a^2 + a^2
Substituting the given side length of the first square, we get: d^2 = 1^2 + 1^2
Simplifying this equation, we have: d^2 = 1 + 1
d^2 = 2
To find the value of d (the diagonal of the first square), we take the square root of both sides: d = √2
Therefore, the diagonal of the first square is √2 meters.
Now, according to the problem statement, the diagonal of the second square is equal to the side length of the first square, which is 1m.
So, the diagonal of the second square is also 1 meter.