Question

1. if $\triangle dgh \sim \triangle def$, find the value of $x$.

Explanation:

Step1: Set up proportion from similarity

Since \(\triangle DGH \sim \triangle DEF\), corresponding sides are proportional. So \(\frac{x + 3}{52}=\frac{2x - 1}{91}\).

Step2: Cross - multiply

Cross - multiplying gives \(91(x + 3)=52(2x - 1)\).

Step3: Expand both sides

Expanding the left side: \(91x+273\), and the right side: \(104x - 52\). So we have the equation \(91x + 273=104x-52\).

Step4: Move like terms together

Subtract \(91x\) from both sides: \(273 = 104x-91x - 52\), which simplifies to \(273=13x - 52\). Then add 52 to both sides: \(273 + 52=13x\), so \(325 = 13x\).

Step5: Solve for x

Divide both sides by 13: \(x=\frac{325}{13}=25\).

Answer:

\(x = 25\)