ABD is a right-angled triangle, whose ∠D is the right angle. C is any point on the side BD. If AB = 8 cm, BC = 6 cm and AC = 3 cm, then the length of CD is : 1. cm 2. cm 3. cm 4. cm

Question

KnowledgeBoat · Accepted Answer

Let CD = x cm BD = BC + CD = (6 + x) cm In △ ABD, using Pythagorean theorem, Hypotenuse2 = Base2 + Height2 ⇒ AB2 = BD2 + AD2 ⇒ 82 = (6 + x)2 + AD2 ⇒ 64 - (6 + x)2 = AD2 ⇒ AD2 = 64 - (6 + x)2 ⇒ AD2 = 64 - (36 + x2 + 12x) ⇒ AD2 = 64 - 36 - x2 - 12x ⇒ AD2 = 28 - x2 - 12x .....(1) In △ ADC, using Pythagorean theorem, ⇒ AC2 = CD2 + AD2 ⇒ 32 = x2 + AD2 ⇒ 9 = x2 + AD2 ⇒ AD2 = 9 - x2 .....(2) From eq.(1) and (2), we have : ⇒ 9 - x2 = 28 - x2 - 12x ⇒ 9 = 28 - 12x ⇒ 12x = 28 - 9 ⇒ 12x = 19 ⇒ x = ⇒ x = cm. Hence, option 1 is the correct option.

Mathematics

ABD is a right-angled triangle, whose ∠D is the right angle. C is any point on the side BD. If AB = 8 cm, BC = 6 cm and AC = 3 cm, then the length of CD is : 1. cm 2. cm 3. cm 4. cm

Pythagoras Theorem

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