Question

prove that c to ab pls.

Answer 1

Sol: Triangle ABC is right angled at C.Let BC = a, CA = b, AB = c. 

i) Area of ΔABC = 1/2 × Base × Height = 1/2 × BC × AC = 1/2 ab     Area of ΔABC = 1/2 × Base × Height = 1/2 × AB × CD = 1/2 cp     ⇒ 1/2 ab = 1/2 cp     ⇒ ab = cp     Hence proved.

 (ii) In right angled triangle ABC,AB2 = BC2 + AC2 c2 = a2 + b2 (ab/p)2 = a2+ b2 a2b2/p2 = a2 + b2 -------- From proof (1)1/p2 = (a2 + b2) / a2b2 1/p2 = (a2 / a2b2 + b2/ a2b2) 1/p2 = (1/b2 + 1/a2) 1/p2 = (1/a2+ 1/b2) Hence proved.