A rectangle, one side of which is 8cm less than the side of the square, and the other twice as large as the side

A rectangle, one side of which is 8cm less than the side of the square, and the other twice as large as the side of the square, has an area equal to the area of this square. Find the sides of a rectangle

Let us denote by a the side of the square. in terms of the variable a, we express the sides of the rectangle, based on the conditions of the problem:

1) One side is 8 cm less than the side of the square, which means that the side of the rectangle is a – 8;

2) The second side is 2 times the side of the square, so. the side of the square is 2a;

3) It is known. that the areas of these figures are equal. Let’s make the equation:

(a – 8) * 2a = a * a;

4) Let us arrange this equation by expanding the brackets:

2a * a – 16a = a * a;

a * a – 16a = 0;

a * (a – 16) = 0;

This means that the side of the square is 16 cm.

This means that one side of the rectangle is 8 and the other is 32.