The perimeter of the triangle is 40 dm. find the area of a rectangle if its length is 3 times its width.

It is known that the perimeter of a rectangle is 40. The perimeter is the sum of the lengths of all sides, which means that the perimeter = 2 * (length + width).

Let x be the width of the rectangle. The condition says that the length is 3 times the width, which means that the width is 3 * x.

Find the sides of the rectangle:

2 * (x + 3x) = 40;

Divide both sides of the equation by 2:

3x + x = 20;

Let’s simplify the equation:

4x = 20;

x = 5; So the width is 5 and the length is 15.

Area = length * width = 15 * 5 = 75 dm;

Answer: the area of the rectangle is 75 dm.