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Question
In the given figure, AB//CD, AB = 7 cm, BD = 25 cm and CD = 17 cm;
find the length of side BC.
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Solution
Take M to be the point on CD such that AB = DM.
So DM = 7cm and MC = 10 cm
Join points B and M to form the line segment BM.
So BM || AD also BM = AD.
In right-angled ΔBAD,
BD2 = AD2 + BA2
(25)2 = AD2 + (7)2
AD2 = (25)2 - (7)2
AD2 = 576
AD = 24
In right-angled ΔCMB,
CB2 = CM2 + MB2
CB2 = (10)2 + (24)2 ...[ MB = AD ]
CB2 = 100 + 576
CB2 = 676
CB = 26 cm
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