To find the side length of a square given its diagonal, we can use the relationship between the side length and the diagonal of a square.
For a square, if the side length is [tex]\( s \)[/tex] and the diagonal is [tex]\( d \)[/tex], the relationship is given by the Pythagorean theorem:
[tex]\[ d = s \sqrt{2} \][/tex]
In this problem, we are given the diagonal [tex]\( d \)[/tex] as [tex]\( 15 \sqrt{2} \)[/tex] cm. Let’s find the side length [tex]\( s \)[/tex].
1. We start with the equation relating the diagonal and the side length:
[tex]\[ d = s \sqrt{2} \][/tex]
2. Substitute the given diagonal length into the equation:
[tex]\[ 15 \sqrt{2} = s \sqrt{2} \][/tex]
3. To solve for [tex]\( s \)[/tex], divide both sides of the equation by [tex]\( \sqrt{2} \)[/tex]:
[tex]\[ s = \frac{15 \sqrt{2}}{\sqrt{2}} \][/tex]
4. Simplifying the fraction by canceling out [tex]\( \sqrt{2} \)[/tex] in the numerator and the denominator, we get:
[tex]\[ s = 15 \][/tex]
Therefore, the side length of the square is [tex]\( 15 \)[/tex] cm.
