To find the approximate length of the diagonal of a square when the perimeter is given, we can follow these step-by-step instructions:
1. Identify the perimeter of the square: Here, the perimeter is given as 68 feet.
2. Calculate the side length of the square:
- The formula for the perimeter of a square is [tex]\( P = 4s \)[/tex], where [tex]\( P \)[/tex] is the perimeter and [tex]\( s \)[/tex] is the side length.
- Rearrange the formula to solve for [tex]\( s \)[/tex]:
[tex]\[ s = \frac{P}{4} \][/tex]
- Substitute the given perimeter into the equation:
[tex]\[ s = \frac{68}{4} = 17 \text{ feet} \][/tex]
So, the side length of the square is 17 feet.
3. Calculate the length of the diagonal:
- The diagonal of a square can be found using the Pythagorean theorem. For a square, if each side is [tex]\( s \)[/tex], then the diagonal [tex]\( d \)[/tex] can be calculated using:
[tex]\[ d = \sqrt{s^2 + s^2} = \sqrt{2s^2} \][/tex]
- Substitute the side length we found earlier into the equation:
[tex]\[ d = \sqrt{2 \times (17^2)} = \sqrt{2 \times 289} = \sqrt{578} \approx 24.041630560342615 \text{ feet} \][/tex]
So, the approximate length of the diagonal of the square is 24.041630560342615 feet.
