Question

13 fill in the blank 1 point a square has a diagonal of length $10\sqrt{2}$, what is the length of a side of the square? side = choose your answer...

Explanation:

Step1: Recall the formula for the diagonal of a square

For a square with side length \( s \), the diagonal \( d \) is related to the side length by the Pythagorean theorem. In a square, the diagonal forms a right triangle with two sides, so \( d = s\sqrt{2} \) (since \( a = s \), \( b = s \), and \( d=\sqrt{a^{2}+b^{2}}=\sqrt{s^{2}+s^{2}}=\sqrt{2s^{2}} = s\sqrt{2} \)).

Step2: Solve for the side length \( s \)

We know that \( d = 10\sqrt{2} \) and \( d = s\sqrt{2} \). So we can set up the equation:
\( s\sqrt{2}=10\sqrt{2} \)
Divide both sides of the equation by \( \sqrt{2} \):
\( s=\frac{10\sqrt{2}}{\sqrt{2}} \)
The \( \sqrt{2} \) terms cancel out, so \( s = 10 \).

Answer:

10