Question

1. what is the missing side length with the given scale factor. scale factor: 1.5 diagram: quadrilateral abcd with sides dc=10, cb=12, da=13; scaled quadrilateral wxyz with zy=15, wx=24, xy=m scale factor: 0.5 diagram: rectangle abcd with sides 6 in, 8 in; scaled rectangle with sides 3 in, x

Explanation:

First Sub - Question (Scale Factor 1.5)

Step1: Identify Corresponding Sides

In similar figures, corresponding sides are proportional. The side of length 12 in the first quadrilateral corresponds to side \( m \) in the second quadrilateral, and the scale factor is 1.5. This means the length of the side in the second figure is the length of the corresponding side in the first figure multiplied by the scale factor.

Step2: Calculate \( m \)

We know that if the original side length is \( s = 12 \) and the scale factor \( k=1.5 \), then the new side length \( m=k\times s \).
So \( m = 1.5\times12 \)
\( m=18 \)

Second Sub - Question (Scale Factor 0.5)

Step1: Identify Corresponding Sides

The side of length 8 in the larger rectangle corresponds to side \( x \) in the smaller rectangle, and the scale factor is 0.5. So the length of the side in the smaller figure is the length of the corresponding side in the larger figure multiplied by the scale factor.

Step2: Calculate \( x \)

Given the original side length \( S = 8 \) and scale factor \( k = 0.5 \), then \( x=k\times S \)
\( x=0.5\times8 \)
\( x = 4 \)

Answer:

For the first sub - question (finding \( m \)): \( m = 18 \)
For the second sub - question (finding \( x \)): \( x = 4 \)