Find the diagonal of a rectangle if its sides are 1: 2 and the perimeter is 18 cm.

We start the solution by calculating the sides of the rectangle. We introduce the coefficient of similarity k and get k and 2k – the sides of the rectangle.

Then we compose the equation:

P = 2 (a + b);

2 (k + 2k) = 18;

3k = 18: 2;

3k = 9;

k = 9: 3;

k = 3.

The sides of the rectangle are 1 * 3 = 3 cm and 2 * 3 = 6 cm.

To find the length of the diagonal, we apply the Pythagorean theorem for a right-angled triangle formed by the sides and the diagonal (hypotenuse).

c ^ 2 = a ^ 2 + b ^ 2;

Substitute values and perform calculations:

c = √ (3 ^ 2 + 6 ^ 2) = √ (9 + 36) = √45 = 3√5 cm.