Question

find the length x.

Explanation:

Step1: Use similar - triangles property

Since the two right - angled triangles are similar, the ratios of their corresponding sides are equal. The ratio of the vertical sides is equal to the ratio of the horizontal sides. So, $\frac{4}{3}=\frac{6}{x}$.

Step2: Cross - multiply to solve for x

Cross - multiplying gives $4x = 3\times6$.

Step3: Simplify the right - hand side

$4x=18$.

Step4: Solve for x

$x=\frac{18}{4}=\frac{9}{2}=4.5$.

Answer:

$4.5$