Question

find the length x.

Explanation:

Step1: Identify similar triangles

The two right - angled triangles are similar.

Step2: Set up proportion

Since the triangles are similar, the ratios of corresponding sides are equal. We have $\frac{x}{3.5}=\frac{8}{x}$.

Step3: Cross - multiply

Cross - multiplying gives us $x^{2}=3.5\times8$.
$x^{2}=28$.

Step4: Solve for x

Taking the square root of both sides, $x = \sqrt{28}=2\sqrt{7}\approx5.29$.

Answer:

$2\sqrt{7}\approx5.29$