Elna has eight rods, each approximately $10$ cm long. She uses these rods to form a rectangle that is three rods long and one rod wide. We want to determine something about the rectangle, but the problem is incomplete, or maybe we are asked about the possible range of perimeter given the approximation "correct to the nearest centimetre".

1. Problem Description

Elna has eight rods, each approximately $10$ cm long. She uses these rods to form a rectangle that is three rods long and one rod wide. We want to determine something about the rectangle, but the problem is incomplete, or maybe we are asked about the possible range of perimeter given the approximation "correct to the nearest centimetre".

2. Solution Steps

Since each rod is $10$ cm long "correct to the nearest centimetre", this means each rod's length, $l$, satisfies $9.5 \le l < 10.5$.

The rectangle is three rods long, so the length of the rectangle $L$ is $3l$. This means $3(9.5) \le L < 3(10.5)$, so $28.5 \le L < 31.5$.

The rectangle is one rod wide, so the width of the rectangle $W$ satisfies $9.5 \le W < 10.5$.

The perimeter of the rectangle is $P = 2L + 2W$.

Therefore, $2(28.5) + 2(9.5) \le P < 2(31.5) + 2(10.5)$.

So, $57 + 19 \le P < 63 + 21$.

$76 \le P < 84$.

The eight rods used have a total length between $8(9.5) = 76$ and $8(10.5) = 84$.

Since the perimeter is equal to the sum of lengths of rods used, that matches.

3. Final Answer

The perimeter of the rectangle is between 76 cm and 84 cm.