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, drawn to the base, is equal to a. Find the side.

1. A, B, C the vertices of the triangle. Angle B is 4 times greater than angle A. BM is the median.

2. We take the value of the angle A and the angle C equal to it as x. Angle B is 4x.

3. Let’s make the equation:

x + x + 4x = 180;

x = 30.

Angle A = 30 °.

4. Triangle ABM is rectangular, since the median BM is also the height.

5. The leg of the BM is opposite an angle of 30 °. Therefore, its length is 2 times less than the length of the hypotenuse AB.

6. Considering this, the length of the hypotenuse AB = BM x 2 = 2a.

Answer: the lateral side AB of triangle ABC is equal to 2a.