Question

find the value of x .
(image of a right triangle with segments: st = 5 m, tv = 9 m, vw = 6 m, and uv = x m, right angles at t and v)
x = | 3 ×

Explanation:

Step1: Use the similarity of triangles

Since \(\triangle STW\sim\triangle UVW\) (by AA similarity as \(\angle T=\angle V = 90^{\circ}\) and \(\angle W\) is common), we can set up the proportion \(\frac{ST}{UV}=\frac{TW}{VW}\).

Step2: Substitute the values

We know \(ST = 5\), \(TW=9 + 6=15\), \(VW = 6\), and \(UV=x\). So the proportion becomes \(\frac{5}{x}=\frac{15}{6}\).

Step3: Cross - multiply

Cross - multiplying gives \(15x=5\times6\).

Step4: Solve for \(x\)

\(15x = 30\), then \(x=\frac{30}{15}=2\).

Answer:

\(x = 2\)