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Question 111947

Question 111947

A garden is of the shape \(ABCDE\) as shown in the diagram below. \(AB\) and \(DC\)are perpendicular to \(BC\). It is given that \(AE=DE=5x\)m , \(AB=DC=y\)m and \(BC=6x\)m.

  1. Find an expression, in terms of \(x\), for the length of \(EK\).
  2. The perimeter and area of the garden are \(54\)m and \(180\)m\(^{2}\) respectively. Write down a pair of simultaneous equations relating \(x\) and \(y\).
  3. Solve the pair of simultaneous equations to find the values of \(x\) and \(y\).

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Answer:\(x = 2, y = 11\) or \(x = \frac{5}{2}, y = 7\)

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