Question

the perimeter o DOG is 33. If DO = 10 and DG = 12, find the larger of the two segments into which the third side is divided by the angle bisector of ODG

Answer 1

The size of the larger of the two segments = 6

Explanation:

Attached below is the triangle ( DOG )

perimeter of Triangle = 33

DO = 10

DG = 12

OG = x

formula for perimeter = DO + DG + OG = 33

= 10 + 12 + OG = 33

hence: OG = 33 - ( 10 + 12 ) = 33 - 22 = 11

third side ( x ) = 11

Finally determine the length of the larger of the two segments of side ( OG)

from the diagram below

`(y')/(x') = (12)/(10)` -------------------- ( 1 )

where x' = 11 - y'

hence equation 1 becomes

10y' = 12x'

10y' = 12 ( 11 - y' )

10y' = 132 - 12y'

22y' = 132

∴ y' = 132 / 22 = 6

hence x' = 5