Question

trapezoid h is a scaled copy of trapezoid g. what is the value of x?

Explanation:

Step1: Find the scale factor

Since trapezoid \(H\) is a scaled copy of trapezoid \(G\), we can find the scale factor using the corresponding sides \(20\) and \(25\) (or \(40\) and \(50\)). The scale factor \(k=\frac{25}{20}=\frac{5}{4}\) (using \(20\) and \(25\): \(\frac{\text{side in }H}{\text{side in }G}\)).

Step2: Calculate \(x\)

We know that the side of length \(24\) in trapezoid \(G\) corresponds to \(x\) in trapezoid \(H\). Using the scale - factor formula \(x = 24\times k\). Substitute \(k=\frac{5}{4}\) into the formula: \(x=24\times\frac{5}{4}\).

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Answer:

\(30\)