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.

$\Rightarrow \frac{DE}{EF} =\frac{LM}{MN}$

$\Rightarrow \frac{6x-9}{4x+4} =\frac{14}{16}$

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.