Mathematics
In the given figure, AB // CD, AB = 7 cm, BD = 25 cm and CD = 17 cm; find the length of side BC.
Pythagoras Theorem
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Answer
In right-angled triangle ABD,
By pythagoras theorem,
⇒ (Hypotenuse)2 = (Perpendicular)2 + Base2
⇒ BD2 = AD2 + AB2
⇒ 252 = AD2 + 72
⇒ 625 = AD2 + 49
⇒ AD2 = 625 - 49
⇒ AD2 = 576
⇒ AD = = 24 cm.
Draw BE perpendicular to CD.
From figure,
ABED is a rectangle. Since, opposite sides of rectangle are equal.
∴ ED = AB = 7 cm and BE = AD = 24 cm.
⇒ CE = CD - ED = 17 - 7 = 10 cm.
In right-angled triangle BEC,
By pythagoras theorem,
⇒ (Hypotenuse)2 = (Perpendicular)2 + Base2
⇒ BC2 = BE2 + CE2
⇒ BC2 = 242 + 102
⇒ BC2 = 576 + 100
⇒ BC2 = 676
⇒ BC = = 26 cm.
Hence, BC = 26 cm.
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