7he width and height of a rectangle are in a ratio of .
a. Draw the rectangle, and divide its width and length into
parts according to its aspect ratio.
b. If the rectangle’s perimeter is 220 cm , find its width
and its height.

Problem Statement

Solution

Part a: Drawing and Dividing the Rectangle According to the Aspect Ratio

• The aspect ratio of the rectangle is given as . This means that for every 9 units of width, there are 2 units of height.

1. Draw the Rectangle:
   • Begin by drawing a rectangle. The orientation (landscape or portrait) can be chosen based on convenience, but typically, the longer side represents the width.
2. Divide the Width into 9 Equal Parts:
   • Since the width is in a ratio of 9, divide the entire length of the width into 9 equal segments. You can mark these divisions using a ruler or by eye, ensuring each part is of equal length.
3. Divide the Height into 2 Equal Parts:
   • Similarly, divide the height of the rectangle into 2 equal segments, reflecting the ratio.
4. Visualization:
   • If you imagine the rectangle as a grid, the width will have 9 columns and the height will have 2 rows. This grid helps in visualizing the proportion between the width and height.

+-------------------------+
|                         |
|                         |
+-------------------------+

• Width: Divided into 9 segments.
• Height: Divided into 2 segments.

Part b: Finding the Width and Height from the Perimeter

• Perimeter §: 220 cm
• Aspect Ratio: Width : Height = 9 : 2

• Let be the width.
• Let be the height.
• Let the common multiplier be . Therefore:

• Width ( ) = 90 cm
• Height ( ) = 20 cm

Conclusion

• Width of the rectangle is 90 cm
• Height of the rectangle is 20 cm