# A circle is inscribed in the quadrilateral ABCD. AB = 5, 2CD = AB. Find the perimeter of a quadrilateral ABCD.

By the problem statement, a circle is inscribed in the quadrilateral ABCD.

You can inscribe a circle into a quadrilateral provided that the sums of the lengths of the opposite sides of this quadrilateral are equal.

Thus, for the specified quadrilateral ABCD, the following equality can be written.

AB + BC = AD + DC.

In order to find the perimeter of a given quadrilateral, you first need to write down the formula by which we calculate the perimeter.

At the same time, remember that the perimeter is the sum of all sides of a certain figure.

P = AB + BC + AD + CD.

Since AB + BC = AD + CD, this formula can be written in another way.

P = 2AB + 2 CD.

Now we substitute the numerical values AB and CD into the indicated formula, and then calculate what the corresponding perimeter is.

P = 2 × 5 + 5 = 10 + 5 = 15 (cm).

Answer: 15 cm.