Question

ABC is a right triangle, right angled at C. let BC=a,CA=b,AB=c and let p be the length of the perpendicular frm C on AB. Prove that 1)cp=ab 2) 1/p2=1/a2 + 1/b2

Answer 1

Answer:

Step-by-step explanation:

1.Area is 1/2 base * height . So for the same triangle area can be 1/2*b*a and can be 1/2*p*c. Hence cp = ab

2 . From above p2 = a2b2/c2

1/p2 = c2/ a2b2

but for right triangle c2 = a2 +b2

Hence 1/p2 = (a2+b2)/ a2b2

Hence 1/p2 = 1/a2+1/b2