To determine the maximum curtain height for a square wall with an area of [tex]\(\frac{289}{64}\)[/tex] square meters, follow these steps:
1. Find the Area of the Square:
The area of the square wall is given as [tex]\(\frac{289}{64}\)[/tex] square meters.
2. Determine the Side Length:
For a square, the area is given by the formula:
[tex]\[
\text{Area} = \text{side}^2
\][/tex]
Given that the area is [tex]\(\frac{289}{64}\)[/tex], we can find the side length by taking the square root of the area:
[tex]\[
\text{side} = \sqrt{\frac{289}{64}}
\][/tex]
3. Calculate [tex]\( \sqrt{\frac{289}{64}} \)[/tex]:
[tex]\(\frac{289}{64}\)[/tex] can be simplified by taking the square roots of the numerator and the denominator separately:
[tex]\[
\sqrt{\frac{289}{64}} = \frac{\sqrt{289}}{\sqrt{64}}
\][/tex]
We know that:
[tex]\[
\sqrt{289} = 17 \quad \text{and} \quad \sqrt{64} = 8
\][/tex]
Therefore:
[tex]\[
\sqrt{\frac{289}{64}} = \frac{17}{8}
\][/tex]
4. Simplify the Side Length:
[tex]\[
\frac{17}{8} = 2.125
\][/tex]
5. Determine the Curtain Height:
Since the curtain height should be the same as the side length of the square wall, the maximum curtain height is:
[tex]\[
\text{Curtain Height} = 2.125 \, \text{meters}
\][/tex]
So, the maximum curtain height for the square wall with an area of [tex]\(\frac{289}{64}\)[/tex] square meters is [tex]\(2.125\)[/tex] meters.
