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In the figure, ABCD is a rectangle and G...


In the figure, `ABCD` is a rectangle and `G` is the centroid of the triangle `ABC.` If `BG = 4 cm,` then find the length of ` AC. `

A

`"12 cm"`

B

`"13 cm"`

C

`"14 cm"`

D

`"15 cm"`

Text Solution

Verified by Experts

The correct Answer is:
A
We know that, the centroid of a triangle divides each median in the ratio of `2:1` from the vertex.
Given, `BG= 4 cm.`
`OG=(1)/(2)(4 cm ) =2 cm `
`implies BO=BG+OG=6 cm`
`impliesBO=OD( :. " Diagonals bisect each other ")`.
`implies OD= 6cm`
`BD=BO+OD=6cm+6cm=12`
But AC=BD (`:.` Diagonals are equal .)
`implies AC=12 cm `
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