To find the side of a square given its diagonal, we can use the relationship between the side length and the diagonal of a square.
1. Identify the relationship: In a square, the diagonal divides it into two right-angled triangles. Hence, the Pythagorean theorem applies. The relationship between the side [tex]\( s \)[/tex] of the square and the diagonal [tex]\( d \)[/tex] is given by:
[tex]\[
d = s\sqrt{2}
\][/tex]
2. Isolate s: Solving for the side length [tex]\( s \)[/tex], we get:
[tex]\[
s = \frac{d}{\sqrt{2}}
\][/tex]
3. Substitute the given diagonal: The given diagonal [tex]\( d = 12\sqrt{10} \)[/tex] feet.
4. Calculate the side length:
[tex]\[
s = \frac{12\sqrt{10}}{\sqrt{2}}
\][/tex]
5. Simplify the expression:
[tex]\[
\frac{12\sqrt{10}}{\sqrt{2}} = 12 \times \frac{\sqrt{10}}{\sqrt{2}} = 12 \times \sqrt{\frac{10}{2}} = 12 \times \sqrt{5}
\][/tex]
[tex]\[
s = 12 \times \sqrt{5}
\][/tex]
6. Evaluate the numerical value: The value of [tex]\( 12\sqrt{5} \)[/tex]:
Based on the given data and through the steps we’ve taken, the calculation gives us:
[tex]\[
s \approx 26.8328 \text{ feet}
\][/tex]
So, the side length of the square is approximately [tex]\( 26.8328 \)[/tex] feet.
