Question

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

Explanation:

Step1: Set up proportion

Since the two quadrilaterals are similar, the ratios of corresponding sides are equal. Let's assume the side - length of 6 in the first quadrilateral corresponds to the side - length of 3 in the second quadrilateral, and the side - length of 8 in the first quadrilateral corresponds to \(x\) in the second quadrilateral. The proportion is \(\frac{6}{3}=\frac{8}{x}\).

Step2: Cross - multiply

Cross - multiplying the proportion \(\frac{6}{3}=\frac{8}{x}\) gives us \(6x = 3\times8\).

Step3: Solve for \(x\)

First, calculate \(3\times8 = 24\). Then, we have the equation \(6x=24\). Divide both sides of the equation by 6: \(x=\frac{24}{6}=4\).

Answer:

4