Question

10.x= if \\( \triangle abc \cong \triangle def \\) and \\( de = 10, ef = 13, \\) and \\( df = 16, \\) and \\( ac = 4x - 8, \\) then \\( x = ? \\)

Explanation:

Step1: Use congruent triangles property

Since \(\triangle ABC\cong\triangle DEF\), corresponding sides are equal. So \(AC = DF\).

Step2: Set up the equation

Given \(AC = 4x - 8\) and \(DF=16\), we have the equation \(4x - 8=16\).

Step3: Solve the equation for \(x\)

Add \(8\) to both sides: \(4x-8 + 8=16 + 8\), which simplifies to \(4x=24\).
Divide both sides by \(4\): \(x=\frac{24}{4}\).

Answer:

\(x = 6\)