Find the sides of a rectangle, one of which is twice as large as the other, if its area is equal to the area

Find the sides of a rectangle, one of which is twice as large as the other, if its area is equal to the area of a square with a side of 12dm.

1. A, B, C, D – the vertices of the rectangle. S – area. The side of the rectangle AD is 2 times larger than the side AB.

2. S rectangle = S square = 12 x 12 = 144 decimetres².

2. We take as x the length of the AB side, the length of the AD side – 2x.

Let’s make the equation:

x x 2x = 144;

2x² = 144;

x² = 72;

x = √72 = √36 x 2 = 6√2.

AB = 6√2 decimeters.

AD = AB x 2 = 6√2 x 2 = 12√2 decimeters.

Answer: the sides of the rectangle AB = 6√2 decimeters, AD = 12√2 decimeters.