Question

In as equilateral triangle lmn,the side mn is trisected at o.prove that lo2\lm2=7\9

Answer 1

Answer:

Proved

Step-by-step explanation:

In as equilateral triangle lmn,the side mn is trisected at o.prove that lo2\lm2=7\9

lmn is equilateral trinagle let say sides = a

mn = a  = lm = ln

lm² = a²

if i draw altitude from l at p on mn

then lp = √3a/2   ( √(a² - (a/2)²))

lo² = lp² + op²

=> lo² = (√3a/2)² + (mp - mo)²

=> lo² = (√3a/2)² + (a/2 - a/3)²   (mo = a/3 as it trisects mn)

=> lo² = 3a²/4 + (a/6)²

=> lo² = 3a²/4 + a²/36

=> lo² = 3a²/4 + a²/36

=> lo² = (27a²+ a²)/36

=> lo² = 28a²/36

=> lo² = 7a²/9

=> lo²/a² = 7/9

=> lo²/lm² = 7/9  as lm² = a²

QED