Question

Find value of x, show your work

Answer 1

Here is your answer

$\huge x=\frac{35}{2}cm= 17.5cm$

REASON :
AB//CD

So,

/_A=/_D ... (alternate int. angles)

/_B=/_C ... (alt. int. angles)

So,

Tri.ABE~Tri.DCE... (by AA similarity)

Therefore,

Corresponding sides are proportional

i.e.

$\frac{AE}{DE}=\frac{AB}{DC}$

$\frac{5}{x}=\frac{4}{14}$

$x=\frac{5×14}{4}$

$x=\frac{5×7}{2}$

$x=\frac{35}{2}$

HOPE IT IS USEFUL