2024 JPJC H1 Q1

The diagram shows a garden which is enclosed by a wall \(AH\) and fencing along the boundary \(ABCDEFGH\). The angles at \(B\), \(D\), \(E\), \(F\), \(G\), \(H\) are each right angles and \(FG=20\) m and \(AB=DE=EF=x\) m. It is given that the total length of the fencing is \(70\) m and that the area of the rectangle \(HBCG\) is fifteen times the area of the square \(CDEF\).

1. Show that \(17x^2+15x-500=0\).[3]
2. Find total area of the garden.[2]