solve for x. figures are not necessarily drawn to scale.

Explanation:

Step1: Use the property of similar triangles

Since (\angle E=\angle GHF = 90^{\circ}) and (\angle F) is common to (\triangle DEF) and (\triangle HGF), (\triangle DEF\sim\triangle HGF) by the AA (Angle - Angle) similarity criterion. For similar triangles, the ratios of corresponding sides are equal. So, (\frac{DE}{GH}=\frac{EF}{HF})

Step2: Substitute the given values

We know that (DE = 42), (EF=28 + 21=49), (HF = 21), and (GH=x) Substituting into (\frac{DE}{GH}=\frac{EF}{HF}), we get (\frac{42}{x}=\frac{49}{21})

Step3: Cross - multiply

Cross - multiplying gives (49x=42\times21)

Step4: Solve for (x)

First, calculate (42\times21 = 882). Then (x=\frac{882}{49}=18)

Answer:

(18)