Question

the quadrilaterals abcd and jklm are similar. find the length x of lm.

Explanation:

Step1: Find the scale factor

Since the quadrilaterals are similar, the ratio of corresponding sides is equal. The ratio of side \(AB\) to \(JK\) is \(\frac{3}{4.8}\).
$$\frac{3}{4.8}=\frac{30}{48}=\frac{5}{8}$$

Step2: Use the scale factor to find \(x\)

We know that \(\frac{AD}{JM}=\frac{DC}{LM}\). Substituting the values, \(\frac{3}{4.8}=\frac{5}{x}\). Cross - multiply: \(3x = 4.8\times5\).
$$3x=24$$
Then solve for \(x\): \(x=\frac{24}{3}\).
$$x = 8$$

Answer:

\(x = 8\)