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.
[tex]$\Rightarrow \frac{DE}{EF} =\frac{LM}{MN}[/tex]
[tex]$\Rightarrow \frac{6x-9}{4x+4} =\frac{14}{16}[/tex]
Do cross multiplication.
[tex]$\Rightarrow 16( {6x-9})=14 ({4x+4} )[/tex]
[tex]$\Rightarrow 96x-144=56 x+56[/tex]
Add 144 on both sides.
[tex]$\Rightarrow 96x-144+144=56 x+56+144[/tex]
[tex]$\Rightarrow 96x=56 x+200[/tex]
Subtract 56x from both sides.
[tex]$\Rightarrow 96x-56x=56 x+200-56x[/tex]
[tex]$\Rightarrow 40x=200[/tex]
Divide by 40 on both sides, we get
[tex]$\Rightarrow x=5[/tex]
The value of x is 5.
