In the given figure, in `DeltaABC , DE||BC` so that `AD= (4x - 3) cm , AE= ( 8x-7) cm , BD= (3x-1) cm and CE= (5x-3) cm` . Find the value of x.

Explanation

In `DeltaABC, DE||BC`
`(AD)/(BD)= (AE)/(CE)` ( by Thale's theorem)
`(4x-3)/(3x-1)= (8x-7)/(5x-3)`
( 4x-3) (5x-3) = (8x-7) (3x-1)
` 20x^(2)-27x+9 = 24x^(2)- 29x+7`
` 4x^(2)-2x-2=0`
`2x^(2)-2x+x-1=0`
`2x(x-1)+1(x-1)=0`
(2x+1)(x-1)=0
x=1 or x= `-1/2`
But when `x= -1/2`
`AD= [4xx(-1/2)-3]=-5`
since distance cannot be negative so `x ne -1/2 `
Hence x = 1