Question

quadrilateral s is a scaled copy of quadrilateral r.
quadrilateral r has a side labeled 32 and a bottom side labeled 8. quadrilateral s has a corresponding side labeled 36 and a bottom side labeled t.
what is the value of t?

Explanation:

Step1: Find the scale factor

Since quadrilateral \(S\) is a scaled - copy of quadrilateral \(R\), the ratio of corresponding sides is the same. Let the scale factor \(k=\frac{\text{side in }S}{\text{side in }R}\). Using the non - \(t\) sides: \(k = \frac{36}{32}\)

Step2: Calculate \(t\)

We know that \(t\) in quadrilateral \(S\) corresponds to \(8\) in quadrilateral \(R\). Using the proportion \(\frac{t}{8}=\frac{36}{32}\). Cross - multiply: \(32t=36\times8\). Then \(32t = 288\), and \(t=\frac{288}{32}\)

Answer:

\(9\)