Question
Apply the Pythagorean theorem to find the length of the diagonal of square?
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Answered by
GPT-4o mini
To find the length of the diagonal of a square using the Pythagorean theorem, we can follow these steps:
1. Let the length of a side of the square be \( s \).
2. When you draw the diagonal, it divides the square into two right triangles. Each triangle has two sides equal to the length of the side of the square.
3. According to the Pythagorean theorem, the square of the length of the diagonal \( d \) can be calculated as:
\[
d^2 = s^2 + s^2
\]
4. This simplifies to:
\[
d^2 = 2s^2
\]
5. To find \( d \), take the square root of both sides:
\[
d = \sqrt{2s^2}
\]
6. This can be further simplified to:
\[
d = s\sqrt{2}
\]
So, the length of the diagonal of a square is \( s\sqrt{2} \), where \( s \) is the length of one side of the square.
1. Let the length of a side of the square be \( s \).
2. When you draw the diagonal, it divides the square into two right triangles. Each triangle has two sides equal to the length of the side of the square.
3. According to the Pythagorean theorem, the square of the length of the diagonal \( d \) can be calculated as:
\[
d^2 = s^2 + s^2
\]
4. This simplifies to:
\[
d^2 = 2s^2
\]
5. To find \( d \), take the square root of both sides:
\[
d = \sqrt{2s^2}
\]
6. This can be further simplified to:
\[
d = s\sqrt{2}
\]
So, the length of the diagonal of a square is \( s\sqrt{2} \), where \( s \) is the length of one side of the square.