Plz answer this

Dear Student,

In this figure

AB  | |  CD  | |  EF

And

Given AB= 7.5 cm, DC= y cm, EF= 4.5 cm, BC= x cm and CE= 3 cm

Now in BFE , we know CD  | |  EF , So from basic proportionality theorem , we get

BDDF = BCCEBDDF = x3
So,

BD  =  x and DF  = 3


Now in FBA , we know CD  | |  AB , So from basic proportionality theorem , we get

FDCD = FBABFDCD = FD + DBAB3y = x + 37.5              --------- ( 1 )

And

Now in BFE , we know CD  | |  EF , So from basic proportionality theorem , we get

BCCD = BEEFBCCD = BC + CEEFxy = x + 34.5           y = 4.5x x + 3                 --------- ( 2 )

Now we substitute value from equation 2  , in equation 1 , we get

34.5xx + 3 = x + 37.53x + 94.5x = x + 37.522.5x + 67.5 = 4.5x2 + 13.5x4.5x2 + 13.5x - 22.5x  - 67.5 = 04.5x2 - 9x  - 67.5 = 0x2 -2x  - 15 = 0

From, Splitting the middle term method we get

x2 - 5x  + 3x  - 15  = 0

x ( x  - 5 ) + 3 ( x - 5 ) = 0

( x - 5 ) ( x + 3 ) = 0
So,
= 5  And  - 3 

But side of triangle can't be negative , So

x  = 5  , Substitute that value in equation 2 , we het

y  = 4.5 × 55 + 3 = 22.58 = 22580 = 4516 = 2.8125 
So,

x  = 5  cm
And
y  = 2 13  cm       [Option 4]
​​​​​          16

Regards

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