Question

Hypotenuse AC of right triangle ABC is divided into 3 equal parts. Two line segments parallel
to CB are drawn from the points of division. If BC = 30 cm, then find the sum of lengths of the
two drawn line segments ?​

Answer 1

Answer:

From given information we form our diagram , As :

Here

AG = GE = EC = x ( Say )

And

BC | | DE | | FG

And

BC = 30

and We wants to find DE + FG

From BPT in triangle ABC and BC | | DE , So

AEDE = ACBC⇒AG+ GEDE = AG+ GE + ECBC⇒x+ xDE = x+ x + x30⇒2 xDE = 3 x30⇒2 DE = 330⇒2 DE = 110⇒DE = 20 cm

And

From BPT in triangle ABC and BC | | FG , So

AGFG = ACBC⇒AGFG = AG+ GE + ECBC⇒xFG = x+ x + x30⇒xFG = 3 x30⇒1 FG = 330⇒1 FG = 110⇒FG = 10 cm

So,

DE + FG = 20 + 10 = 30 cm

Therefore,

The sum of lengths of the two drawn line segments = 30 cm ( Ans )