The width of the rectangle is 4/9 of its length, and the perimeter is 13 cm. What is the area of the rectangle.

Find how many centimeters add up to the width and length of the rectangle.
Divide the perimeter by 2.
Will be:
13/2 = 6.5 cm.
We denote the length as a.
Thus, the width of the rectangle will be: 4/9 * a.
We express the length of the shape.
4/9 * a + a = 6.5.
1 4/9 * a = 6.5.
a = 6.5 / 1 4/9 = 6.5 / 13/9 = 6.5 * 9/13 = 58.5 / 13 = 4.5 cm.
So the width will be equal to:
4/9 * 4.5 = 2 cm.
We check:
6.5 – 4.5 = 2 cm.
The area of the rectangle will be:
2 * 4.5 = 9 cm2
Answer: the area of this rectangle is 9 cm2