Question

quadrilateral jklm is similar to quadrilateral nopq. find the measure of side no. round your answer to the nearest tenth if necessary.

Explanation:

Step1: Set up proportion for similar - figures

Since quadrilateral JKLM is similar to quadrilateral NOPQ, the ratios of corresponding sides are equal. Let NO be \(x\). The ratio of the corresponding non - parallel sides gives us the proportion \(\frac{NO}{JK}=\frac{PQ}{LM}\).
We know that \(JK = 7.8\), \(LM = 13\), and \(PQ = 55\).
The proportion is \(\frac{x}{7.8}=\frac{55}{13}\).

Step2: Solve the proportion for \(x\)

Cross - multiply: \(13x=7.8\times55\).
First, calculate \(7.8\times55 = 429\).
Then, solve for \(x\): \(x=\frac{429}{13}\).
\(x = 33\).

Answer:

33