Question

ABC is a right triangle, right angled at C. Let BC=a, CA=b, AB=c and let p be length of perpendicular from C on AB. Prove that

(i) cp=ab

(ii) 1/p2=1/a2+1/b2

answer as quick as possible, tomorrow is my SA- 1 exam.

Answer 1

Answer:

(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.

Step-by-step explanation: