In an obtuse isosceles triangle, one of the corners is four times the size of the other.

In an obtuse isosceles triangle, one of the corners is four times the size of the other. The median of the triangle to the base is a. Find the side.

Since the triangle is isosceles, the angle BAC = BCA. Let the angle BAC = BCA = X0, then, by condition, the angle ABC = 4 * X0.

The sum of the interior angles of the triangle is 1800, then X + X + 4 * X = 180.

6 * X = 180.

X = BAC = BCA = 180/6 = 30.

Then the angle ABC = 30 * 4 = 120.

From the right-angled triangle of the AВD, the leg of the ВD lies opposite the angle 30, and therefore, its length is equal to half the length of the hypotenuse AB, then AB = 2 * ВD = 2 * a cm.

Answer: The side of the triangle is 2 * a cm.