Mathematics
In the figure, given below, AD ⊥ BC. Prove that :
c2 = a2 + b2 - 2ax.
Pythagoras Theorem
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Answer
By formula,
By pythagoras theorem,
⇒ (Hypotenuse)2 = (Perpendicular)2 + (Base)2
In right-angled △ ABD,
⇒ AB2 = AD2 + BD2
⇒ c2 = h2 + (a - x)2 ………….(1)
In right-angled △ ACD,
⇒ AC2 = AD2 + CD2
⇒ b2 = h2 + x2
⇒ h2 = b2 - x2 ……….(2)
Substituting value of h2 from equation (2) in (1), we get :
⇒ c2 = b2 - x2 + (a - x)2
⇒ c2 = b2 - x2 + a2 + x2 - 2ax
⇒ c2 = a2 + b2 - 2ax.
Hence, proved that c2 = a2 + b2 - 2ax.
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