b. write the expression of the perimeter of the rectangle.

The problem states that Figure B is an enlargement of Figure A. This means there is a constant scale factor by which all corresponding lengths of Figure A are multiplied to get the lengths of Figure B.

Choose a pair of corresponding sides for which both lengths are known.

• The left vertical side of Figure A is $7 \text{ cm}$, and the corresponding side of Figure B is $14 \text{ cm}$. The scale factor $k$ is the ratio of the length in Figure B to the length in Figure A:

We can verify this with other corresponding sides:

• Middle vertical side: $\frac{10 \text{ cm}}{5 \text{ cm}} = 2$
• Slanted side: $\frac{6 \text{ cm}}{3 \text{ cm}} = 2$
• Bottom horizontal side: $\frac{8 \text{ cm}}{4 \text{ cm}} = 2$ The scale factor is consistently 2.

The side labeled $x$ in Figure B corresponds to the top horizontal side of Figure A, which is $2 \text{ cm}$.
To find $x$, multiply the corresponding length in Figure A by the scale factor: