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The ratio of the side of a square to its diagonal is 1:√2. (answer in exact form)
i)
What is the length of the diagonal for a square with side 2√2 metres?

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GinnyAnswer

To find the length of the diagonal for a square with a side length of \(\(2\sqrt{2}\)\) meters, we can follow these steps:

1. Understand the ratio:
The ratio of the side of a square to its diagonal is \(\(1:\sqrt{2}\)\). This implies the diagonal \(\(d\)\) of the square can be calculated using the side length \(\(s\)\) with the formula:
\(\[ d = s \sqrt{2} \]\)

2. Given side length:
The side length \(\(s\)\) of the square is \(\(2\sqrt{2}\)\) meters.

3. Calculate the diagonal:
Substitute the side length into the formula to find the diagonal:
\(\[ d = (2\sqrt{2}) \times \sqrt{2} \]\)

4. Simplify the expression:
\(\[ d = 2 \times \sqrt{2} \times \sqrt{2} = 2 \times 2 = 4 \text{ meters} \]\)

Therefore, the length of the diagonal for a square with a side length of \(\(2\sqrt{2}\)\) meters is exactly \(\(4\)\) meters.

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