Question

find the length x.
image of two right triangles with a common hypotenuse, one with legs x and 7, the other with legs 3 and 3.5

Explanation:

Step1: Identify similar triangles

The two right triangles are similar (vertical angles are equal, right angles are equal, so AA similarity applies).

Step2: Set up proportion

Corresponding sides are proportional: $\frac{x}{3} = \frac{7}{3.5}$

Step3: Solve for x

First simplify $\frac{7}{3.5}=2$, then $x = 3 \times 2$

Answer:

$6$