Question

The polygons are similar, but not necessarily drawn to scale. Find the value of x.

Answer 1

If the shapes are similar, the correspondent sides are in proportion:

$AB\div DE = BC \div EF$

Let's plug the values and solve for x:

$5x \div 5 = 4 \div x \iff \dfrac{5x}{5}=\dfrac{4}{x}\iff x = \dfrac{4}{x}$

Multiply both sides by x to get

$x^2=4 \iff x=\pm2$

The only feasible solution, though, is $x=2$, because it wouldn't make sense to have negative lengths.