Question

the polygons shown below are similar. find the scale factor
lmno~rqts
written as a fraction, the scale factor =
x =

Explanation:

Step1: Determine the scale factor

The scale factor is the ratio of the corresponding sides of the smaller polygon to the larger polygon.
$$\text{Scale factor}=\frac{9.8}{14}$$
Simplify the fraction:
$$\frac{9.8}{14}=\frac{98}{140}=\frac{7}{10}$$

Step2: Find the value of \(x\)

Since the polygons are similar, the ratio of their corresponding sides is equal to the scale factor.
$$\frac{x}{11.5}=\frac{7}{10}$$
Cross - multiply:
$$10x = 11.5\times7$$
$$10x=80.5$$
Solve for \(x\):
$$x=\frac{80.5}{10}=8.05$$

Answer:

The scale factor is \(\frac{7}{10}\) and \(x = 8.05\)