Question

question 1
solve for x. figures are not necessarily dra
scale.
answer
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Explanation:

Step1: Use the similarity of triangles

Since \(\angle PHE=\angle PED = 90^{\circ}\) and \(\angle P\) is common, \(\triangle PHE\sim\triangle PED\) (by AA similarity criterion).
For similar triangles, the ratios of corresponding sides are equal. That is \(\frac{PH}{PE}=\frac{x}{ED}\).

Step2: Substitute the values

We know that \(PH = 21\), \(PE=21 + 28=49\), and \(ED = 42\).
Substituting into \(\frac{PH}{PE}=\frac{x}{ED}\), we get \(\frac{21}{49}=\frac{x}{42}\).
Cross - multiply: \(49x=21\times42\).
Since \(21\times42 = 882\), then \(x=\frac{882}{49}\).

Step3: Simplify the fraction

\(x = 18\).

Answer:

\(18\)