In the adjoining figure, find the length of AD in terms of b and c.

Question

KnowledgeBoat · Accepted Answer

In right angle triangle ABC, By pythagoras theorem, BC² = AB² + AC² BC² = c² + b² BC = . From figure, Area of △ABC = Area of △ABD + Area of △ADC ⇒ x AB x AC = x AD x BD + x AD x CD ⇒ (AB.AC) = (AD.BD + AD.CD) ⇒ AB.AC = AD.BD + AD.CD ⇒ AB.AC = AD(BD + CD) ⇒ AB.AC = AD.BC [∵ BD + CD = BC] ⇒ AD = Putting values of AB, AC and BC in above equation we get, AD = Hence, AD = .

Mathematics

In the adjoining figure, find the length of AD in terms of b and c.

Pythagoras Theorem

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Mathematics

In the adjoining figure, find the length of AD in terms of b and c.

Pythagoras Theorem

Related Questions

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ABCD is a square, F is mid-point of AB and BE is one third of BC. If area of △FBE is 108 cm2, find the length of AC.

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In the adjoining figure, △PQR is right angled at Q and points S and T trisect side QR. Prove that
8PT² = 3PR² + 5PS².

In a quadrilateral ABCD, ∠B = 90°. If AD² = AB² + BC² + CD², Prove that ∠ACD = 90°.

ABCD is a square, F is mid-point of AB and BE is one third of BC. If area of △FBE is 108 cm², find the length of AC.

In a triangle ABC, AB = AC and D is a point on side AC such that BC² = AC × CD.
Prove that BD = BC.