The length of the rectangle is 2 times its width. What is the area of a rectangle if its perimeter is 30cm? 15dm? 6cm?

Let the width of the rectangle be b = x, then its length is a = 2 x.

1. Formula for calculating the perimeter of a rectangle:

P = (a + b) 2 = (2 x + x) 2 = 3 x 2 = 6 x.

2. Determine the values of the unknown x (the width of the rectangle) and its length for

different perimeter values:

x = b = P: 6,

P1 = 30 cm, x1 = b1 = 30: 6 = 5 cm, a1 = 2 x1 = 2 5 = 10 cm;

P2 = 15 dm, x2 = b2 = 15: 6 = 2.5 dm, a2 = 2 2.5 = 5 dm;

P3 = 6 cm, x3 = b3 = 6: 6 = 1 cm, a3 = 2 1 = 2 cm.

3. Let’s calculate the values of the areas:

S1 = a1 b1 = 10 5 = 50 cm ^ 2;

S2 = a2 b2 = 5 2.5 = 12.5 dm ^ 2;

S3 = a3 b3 = 2 1 = 2 cm ^ 2.