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Rectilinear Figures, SM-Bank 015

The length of this rectangle is one and a half times its height.
 

The perimeter of the rectangle is 40 centimetres.

What are the dimensions of the rectangle?  (2 marks)

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\(\text{Height}=8\ \text{cm}\)

\(\text{Length}=12\ \text{cm}\)

Show Worked Solution
\(\text{Let}\ \ \ x\) \(=\text{height}\)
\(\dfrac{3}{2}x\) \(=\text{length}\)
\(2\times \Big(x +\dfrac{3}{2}x\Big)\) \(= 40\)
\(2\times \Big(\dfrac{5x}{2}\Big)\) \(= 40\)
\(5x\) \(= 40\)
\(x\) \(= 8\)
\(\therefore\ \text{Height}\) \(= 8\ \text{cm}\)
\(\therefore\ \text{Length}\) \(=\dfrac{3}{2}\times 8\)
  \(=12\ \text{cm}\)