A farmer wants to fence off a perfectly square paddock for grazing sheep, and cannot order the right length of fencing panels until she knows the paddock's ...
Question 1 Report
A farmer wants to fence off a perfectly square paddock for grazing sheep, and cannot order the right length of fencing panels until she knows the paddock's dimensions. Its area comes to \(324 \text{ m}^2\).
- Given that side squared equals \(324\), find the side length of the paddock, in metres. (2)
- A second, smaller paddock has an area of \(196 \text{ m}^2\). Find its side length. (1)
Answer Details
Both parts find the side length of a square field from its area by taking a square root.
- (a) [2]. \(\sqrt{324} = 18\) m, since \(18\times18 = 324\). One mark for identifying the square root as the correct operation, one for the value \(18\) m.
- (b) [1]. \(\sqrt{196} = 14\) m, since \(14\times14 = 196\).
For a square paddock, area \(=\) side\(^2\), so reversing this with a square root always gives the fencing length needed for one side.
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