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ABC is a right triangle, right-angled at C. If p is the length of the perpendicular from CtoAB and a, b, c have the usual meaning, then prove that:25.アー區+豆 |
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Answer» Triangle ABC is right angled at C.Let BC = a, CA = b, AB = c. (i) Area ofΔABC = 1/2 × Base × Height = 1/2 × BC × AC = 1/2ab Area ofΔABC = 1/2 × Base × Height = 1/2 × AB × CD = 1/2cp⇒1/2ab= 1/2cp⇒ab=cp Hence proved. (ii) In right angled triangle ABC,AB^2= BC^2+AC^2c^2=a^2+b^2(ab/ p)^2=a^2+b^2a^2b^2/p^2=a^2+b^2-------- From proof (1)1/p^2= (a^2+b^2) /a^2b^21/p^2= (a^2/a^2b^2+b^2/a^2b^2)1/p^2= (1/b^2+ 1/a^2)1/p^2= (1/a^2+ 1/b^2) Hence proved. |
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