# In a rectangle, the diagonal divides the angles in a ratio of 1: 2; the smaller side is equal to 5 find its diagonal.

In a rectangle, the diagonal divides the angles in a ratio of 1: 2; the smaller side is equal to 5 find its diagonal. Only do not solve by the theorem of sines, we have not studied the Pythagorean theorem yet.

Let the value of the angle CBD = X0, then, by condition, the value of the angle ABD = 2 * X0.

Since ABCD is a rectangle, the angle ABC = 90, then the angle (ABD + CBD) = (2 * X + X) = 90.

3 * X = 90.

X = CBD = 90/3 = 30, then the angle ABD = 2 * 30 = 60

In a right-angled triangle ABD, we determine the length of the hypotenuse BD.

CosABD = AB / BD.

BD = AB / Cos60 = 5 / (1/2) = 10 cm.

Answer: The length of the diagonal is 10 cm.

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