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 )?
( 23\times4 = 92 )
a is 4 times as long as b
b is 23 times as long as c
c:a
( a:b = 4 )
( b:c = 23 )
a is 92 times as long as

Explanation:

Step1: Express the relationships

Given \(A:B = 4\), so \(A = 4B\). Given \(B:C=23\), so \(B = 23C\).

Step2: Substitute \(B\) in terms of \(C\) into the equation for \(A\)

Substitute \(B = 23C\) into \(A = 4B\). Then \(A=4\times(23C)=92C\).

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

If \(A = 92C\), then \(C=\frac{1}{92}A\).

Answer:

The scale factor that scales \(C\) to \(A\) is \(\frac{1}{92}\)