Question

1. trapezoids defg and jklm are similar. which proportion must be true?

a. \\(\frac{16}{x} = \frac{48}{12}\\)
b. \\(\frac{48}{x} = \frac{16}{12}\\)
c. \\(\frac{16}{x} = \frac{12}{48}\\)
d. \\(\frac{12}{x} = \frac{16}{48}\\)
(image of trapezoids defg and jklm: defg has side gd = 48 m, top gf = x m; jklm has side mj = 12 m, top ml = 16 m)

Explanation:

Step1: Recall Similar Figures Property

For similar figures, corresponding sides are proportional. In trapezoids DEFG and JKLM, side \( GF \) (length \( x \)) corresponds to side \( ML \) (length 16 m), and side \( DG \) (length 48 m) corresponds to side \( MJ \) (length 12 m).

Step2: Set Up Proportion

The ratio of corresponding sides should be equal. So, \( \frac{\text{Side of DEFG}}{\text{Side of JKLM}}=\frac{\text{Corresponding Side of DEFG}}{\text{Corresponding Side of JKLM}} \). Thus, \( \frac{48}{x}=\frac{16}{12} \) (since \( DG = 48 \) corresponds to \( MJ = 12 \), and \( GF = x \) corresponds to \( ML = 16 \)).

Answer:

B. \(\frac{48}{x} = \frac{16}{12}\)