The length of a rectangle is 4 times its width. Find the area of a rectangle if its width is 12 m less than its length.

The width of the rectangle (a) -? cm, 12 m less than b;

Length of rectangle (b) -? cm, 4 times more than a;

Area (Sp.) -? cm ^ 2.

Knowing from the condition of the ratio between the sides of the rectangle, we express them as follows:

1) b = 4 * a – the length of the rectangle;

2) a = b – 12 – the width of the rectangle;

Substituting the expression for finding the length into the expression for finding the width (simply b in a), we get:

a = 4 * a – 12;

4a – a = 12;

3a = 12;

a = 4 (cm).

Substitute the resulting value of the width of the rectangle into expression (1):

b = 4 * 4 = 16 (cm).

The area of ​​a rectangle (the product of its length and width) is found by the formula:

Sp. = a * b = 4 * 16 = 64 (cm ^ 2).

Answer: the area of ​​the rectangle is 64 cm ^ 2.