Question

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find x.
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Explanation:

Step1: Apply the basic proportionality theorem (Thales' theorem)

If a line is drawn parallel to one side of a triangle intersecting the other two sides, then it divides those sides proportionally. Here, we have \(\frac{x}{27}=\frac{44 + 33}{33}\).

Step2: Simplify the right - hand side of the equation

First, calculate \(44+33 = 77\). So the equation becomes \(\frac{x}{27}=\frac{77}{33}\).

Step3: Cross - multiply to solve for \(x\)

Cross - multiplying gives \(33x=27\times77\). Then \(x=\frac{27\times77}{33}\).

Step4: Simplify the fraction

We know that \(77\div11 = 7\) and \(33\div11 = 3\). So \(x=\frac{27\times7}{3}\). Since \(27\div3 = 9\), then \(x = 9\times7\).

Answer:

\(x = 63\) in.