The sides of the rectangle are 1: 4, and the area is 36. Find the sides.

From the condition it is known that the sides of the rectangle are 1: 4, and it is also known that the area of the rectangle is 36. And we need to find the sides of the rectangle.

To do this, we will compose and solve the equation. Let’s remember the formula for finding the area of a rectangle:

S = a * b.

Let us introduce the coefficient of similarity k. Then we write the lengths of the sides as k and 4k.

Let’s make the equation:

k * 4k = 36;

4k ^ 2 = 36;

k ^ 2 = 9.

k = 3 is the length of the smaller side, then the length of the larger side is 3 * 4 = 12.

Answer: 3 and 12 are the lengths of the sides of the rectangle.