The area of the rectangle is 7, find its larger side if it is 6 more less than the side.

Let us denote by s the length greater than the side of the given 4-gon, all four angles of which are 90 degrees.

In the initial data for this task, it is reported that this side is 6 more than the other side of this geometric figure, therefore, the length of the other side is c – 6.

Also in the condition of the problem it is said that if we multiply the lengths of these two sides, then the result will be 7, therefore, we can compose the following equation:

s * (s – 6) = 7,

solving which, we get:

s² – 6s – 7 = 0;

c = 3 ± √ (9 + 7) = 3 ± √16 = 3 ± 4;

c = 3 + 4 = 7.

Answer: The length of the longer side is 7.