Question

$$\frac{ac}{df} = \frac{bc}{ef}$$ $$\frac{90}{36} = \frac{bc}{38}$$ $$\frac{90}{36} cdot 38 = bc$$ so, side length ( ef ), 38, is multiplied by (\boxed{}) to get corresponding side length ( bc ). thus, side length ( bc ) is equal to (\boxed{}) inches. and side length ( ab ) is equal to (\boxed{}) inches.

Explanation:

Step1: Identify the scale factor

From the proportion \(\frac{90}{36}=\frac{BC}{38}\), the scale factor to multiply \(EF = 38\) by is \(\frac{90}{36}\). Simplify \(\frac{90}{36}=\frac{5}{2}=2.5\).

Step2: Calculate BC

Multiply \(38\) by \(\frac{90}{36}\): \(\frac{90}{36}\times38=\frac{90\times38}{36}=\frac{3420}{36} = 95\).

Answer:

The scale factor is \(\frac{90}{36}\) (or \(2.5\)), and \(BC = 95\) inches.