The diagonal of a rectangle divides its angle 1: 2. Find its length if the sum of both diagonals

The diagonal of a rectangle divides its angle 1: 2. Find its length if the sum of both diagonals and two smaller sides is 24 cm.

We take the x angle between the diagonal and the larger side, since a rectangle is given, we get the equation:

x + 2x = 90;

3x = 90;

x = 30 degrees.

Let us denote by a the smaller side, then the length of the diagonal will be equal to:

a: sin (30) = 2a.

Then we get the expression:

2 * 2a + 2a = 24;

6a = 24;

a = 4.

The length of the required diagonal is: 4 * 2 = 8.