The length of the rectangle is 1.5 times its width. Find the area of a rectangle if its perimeter is 25.

1) Let’s introduce a variable.

x is the width of the rectangle;

1.5x is the length of the rectangle.

2) Let’s make an equation.

The perimeter of a rectangle is equal to the sum of the lengths of its four sides, and is calculated by the formula P = 2 (a + b), where P is the perimeter, a = length, and b is the width.

Let us substitute 1.5x and x in the formula instead of a and b, respectively, and substitute 25 for P. We obtain the equation 2 (1.5x + x) = 25.

3) Solve the equation, and find the length and width of the rectangle.

2 * 2.5x = 25;

5x = 25;

x = 25: 5;

x = 5 – width;

1.5x = 5 * 1.5 = 7.5 – length.

4) Find the area of ​​the rectangle.

The area of ​​a rectangle is equal to the product of its sides and is calculated by the formula S = ab.

S = 5 * 7.5 = 37.5.

Answer. 37.5.