Area, SM-Bank 021

A square has an area of \(81\ \text{cm}^2\).

A rectangle has the same perimeter as the square and has a width of \(15\ \text{cm}\).

What is the length of the rectangle in centimetres? (2 marks)

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\(3\ \text{cm}\)

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\(\text{Area of square} = 81\ \text{cm}^2\)

\(\therefore\ \text{Side length of square}=\sqrt{81}=9\ \text{cm}\)

\(\therefore\ \text{Perimeter of square}=4\times 9=36\ \text{cm}\)

\(\therefore\ \text{Length of rectangle}\)	\(=\dfrac{36-(2\times 15)}{2}\)
	\(=\dfrac{6}{2}\)
	\(=3\ \text{cm}\)