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65. In the adjoining figure (not drawn to scale) AB, EF and CD
are parallel lines. Given that EG=5 cm, GC = 10 cm and
DC = 18 cm. Calculate AC, if AB = 15 cm:
(a) 21 cm
(C) 18 cm
(b) 25 cm
(d) 28 cm
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z00 M, Id:6849304329, P:12345
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ANSWER:
the answer is option b) 25 cm
EXPLANATION:
in triangleCDG and triangleEFG,
angleEFG = angleCDG [alt int angles]
angleEGF = angleCGD [vertically opp angles]
∴ the triangles are similar [BY AAA criteria ]
∴ the sides are proportional
5/10 = EF/18
∴EF = 9 cm -------1
In triangleABC and triangleEFC
angleA= angleE [corresponding angles]
angleB = angleF [ corresponding angles]
∴the triangles are similar [BY AAA criteria]
∴ the sides are proportional
9/15 = 15/AC
AC = 25 cm
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