Question

In ∆ ACE , points B, D and F are the midpoints of each side and .G is the centroid . If BG = 5 cm find GE and BE. 
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Answer 1

Given :- In ∆ACE , points B, D and F are the midpoints of each side and .G is the centroid . If BG = 5 cm find GE and BE. ?

Solution :-

From image we have :-

• in ∆ACE, G is centroid of ∆ .
• B is mid - Point of AC . => EB is median .
• D is mid - Point of CE. => AD is median .
• F is mid - Point of AE. => CF is median .
• BG = 5 cm.

we know that,

• Centroid divides the median in 2 : 1.

So,

→ EG : GB = 2 : 1

Let EG and GB are 2x and x.

given that,

→ GB = 5cm.

so,

→ x = 5cm.

Therefore,

→ GE = 2x = 2 * 5 = 10 cm. (Ans.)

Hence,

→ BE = EG + GB = 10 + 5 = 15 cm (Ans.)

Learn more :-

3.

In the fig, AB || CD,FIND x.(Hint:Prove that AOB-COD).

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