Question

1. there are three rectangles in a similar set: rectangle a, rectangle b, and rectangle c. the following questions are about the lengths of the three rectangles.

a. if a:b = 4 and b:c = 23, then what scale factor would scale c to a?

Explanation:

Step1: Express ratios as fractions

Given \(A:B = 4\) (can be written as \(\frac{A}{B}=4\)) and \(B:C = 23\) (can be written as \(\frac{B}{C}=23\)).

Step2: Find \(\frac{A}{C}\)

Multiply the two fractions: \(\frac{A}{B}\times\frac{B}{C}=\frac{A}{C}\). Substitute the values: \(4\times23=\frac{A}{C}\).

Step3: Find scale factor from \(C\) to \(A\)

The scale factor from \(C\) to \(A\) is \(\frac{A}{C}\). Since \(\frac{A}{C}=4\times23 = 92\).

Answer:

The scale factor that scales \(C\) to \(A\) is \(92\).