Question

find the length x.
diagram of two right triangles with a common hypotenuse, one with legs x and 3, the other with legs 7.5 and 4.5

Explanation:

Step1: Set up proportion (similar triangles)

$\frac{x}{7.5} = \frac{3}{4.5}$

Step2: Solve for x via cross-multiplication

$x = 7.5 \times \frac{3}{4.5}$

Step3: Simplify the expression

$x = 7.5 \times \frac{2}{3}$

Answer:

$5$