Question

7-8 jay enlarged figure a so that it was similar to figure b. his diagram is shown below.

4 mm
7 mm
2 mm a
10 mm
x
5 mm b

a. what is the scale factor?

b. what is the value of x?

Explanation:

Part a: Scale Factor

Step1: Identify corresponding sides

We take the corresponding sides of the two similar figures. For example, the side of length 2 mm in figure A corresponds to 5 mm in figure B, or 4 mm in A corresponds to 10 mm in B.

Step2: Calculate scale factor

Scale factor is the ratio of the length of a side in figure B to the length of the corresponding side in figure A. Using the sides 2 mm (A) and 5 mm (B):
Scale factor $= \frac{5}{2} = 2.5$
(We can also check with 4 mm and 10 mm: $\frac{10}{4} = 2.5$, same result)

Step1: Use scale factor

Since the figures are similar, the ratio of corresponding sides is the scale factor (2.5). The side of length 7 mm in figure A corresponds to side \( x \) in figure B.

Step2: Solve for \( x \)

We know that \( \frac{x}{7} = 2.5 \) (scale factor). Multiply both sides by 7:
\( x = 7 \times 2.5 \)
\( x = 17.5 \)

Answer:

The scale factor is $2.5$ (or $\frac{5}{2}$)

Part b: Value of \( x \)