Question

Please help me ive never done one like this

Answer 1

Given:

DE = (6x - 9) cm

EF = (4x + 4) cm

LM = 14 cm

MN = 16 cm

To find:

The value of x.

Solution:

If three or more parallel lines intersect two transversals, then they cut off the transversals proportionally.

`$\Rightarrow (DE)/(EF) =(LM)/(MN)`

`$\Rightarrow (6x-9)/(4x+4) =(14)/(16)`

Do cross multiplication.

`$\Rightarrow 16( {6x-9})=14 ({4x+4} )`

`$\Rightarrow 96x-144=56 x+56`

Add 144 on both sides.

`$\Rightarrow 96x-144+144=56 x+56+144`

`$\Rightarrow 96x=56 x+200`

Subtract 56x from both sides.

`$\Rightarrow 96x-56x=56 x+200-56x`

`$\Rightarrow 40x=200`

Divide by 40 on both sides, we get

`$\Rightarrow x=5`

The value of x is 5.