Question

question quadrilateral lmno is similar to quadrilateral pqrs. find the measure of side rs. round your answer to the tenth if necessary.

Explanation:

Step1: Find the scale - factor

Since the two quadrilaterals LMNO and PQRS are similar, the ratios of their corresponding sides are equal. Let the scale - factor be \(k\). We can find the scale - factor by comparing the corresponding sides with known lengths. For example, if we compare the sides LO and PS, we have \(k=\frac{LO}{PS}\). Here, \(LO = 31\) and \(PS = 10\), so \(k=\frac{31}{10}=3.1\).

Step2: Calculate the length of RS

We know that the side NO corresponds to RS. Let \(RS=x\). Using the scale - factor, we have the proportion \(\frac{NO}{RS}=k\). Given \(NO = 15\) and \(k = 3.1\), we can rewrite the proportion as \(\frac{15}{x}=3.1\). Solving for \(x\), we get \(x=\frac{15}{3.1}\approx4.8\).

Answer:

4.8