In the following figure AB||CD||EF||GH and BH=100 cm. find x and y.

Explanation

Produce GA and HB, which intersect each other at O.
Now is `DeltaOGH` , since AB||GH.
`(OG)/(OH)=(AG)/(BH)`
(Cor.of B.P. theorem)
Also in ` Delta GH`, Since EF||GH
`(OG)/(OH)= ( EG)/(FH)`
From equations (1) and (2) we, get
` (AG)/(BH)= (EG)/(FH)`
` (90+x)/100 = 50/40`
90+x = 12.5 `Rightarrow x = 125-90= 35 cm `
Similarly, we can write
` (AG)/(BH) = (AC)/(BD) " "` (Cor. of B.P Theorem)
` (90+x)/ 100 = (40)/y Rightarrow 125/100= 40/y`
` y = (100xx40)/125 Rightarrow y = 32 cm `
Hence , x= 35 cm and y = 32 cm.