N2000 P1 Q17
In the diagram, ABCD is a quadrilateral with BA parallel to CD.
AC and BD meet at X, where CX = 8 cm and XA = 10 cm.
(a) Given that BD = 27 cm, find the length BX.
(b) Find the ratio of the area of triangle BXC to the area of triangle AXD.
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Answer:
(a) ΔBXA is similar to ΔDXC (AA)
(angle ABX = angle CDX => alternate angles)
(angle BAX = angle DXX => alternate angles)
Hence, BX/XD = 10/8 = 5/4
Given that BD = BX + XD = 27 cm,
BX = 5/9 * 27 = 15 cm.
(b) XD = 27 cm - 15 cm = 12 cm
Area of ΔBXC = ½(15)(8) sin θ
Area of ΔAXD = ½(10)(12) sin θ
Hence,
Area of ΔBXC / Area of ΔAXD = [ ½(15)(8) sin θ ] / [ ½(10)(12) sin θ ]
= [15 * 8] / [10 * 12]
= 1
