Question

prove that 1/h²=1/a²+1/b²​

Answer 1

Step-by-step explanation:

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.