#### Answer

$x= 8$ units

#### Work Step by Step

Step 1: Since the triangles are similar, their corresponding sides are in
proportion.
Step 2: This means that $\frac{4}{x}=\frac{4}{x}=\frac{7}{14}$.
Step 3: Since the triangle in question is an isosceles triangle, both the unknown x's represent equal lengths. Therefore, we will equate the proportion of any one set of sides containing the unknown with the set of known sides.
Step 4: Therefore, $\frac{4}{x}=\frac{7}{14}$.
Step 5: Solving through cross multiplication: $7x=14\times4$.
Step 6: $7x=56$.
Step 7: $x= 8$ units.
Check:
Step 1: Equating the two proportions to see if they reduce to the same fraction: $\frac{4}{8}=\frac{4}{8}=\frac{7}{14}$.
Step 2: $\frac{1}{2}=\frac{1}{2}=\frac{1}{2}$.
Step 3: Therefore, the answer is accurate.