The bottom of the Mitsubishi cone is an equilateral triangle with side length a, and the length of the two sides is (root number 13) a / 2. Try to find the value range of the third side length

The bottom of the Mitsubishi cone is an equilateral triangle with side length a, and the length of the two sides is (root number 13) a / 2. Try to find the value range of the third side length

Two sides √ 13A / 2 form a side of an isosceles triangle. The bottom of the side is one side of the bottom of the isosceles triangle. The length of the bottom side is a,
So the middle line and height of the side of the isosceles triangle = {(√ 13A / 2) & # 178; - (A / 2) & # 178;} = √ 3a
One height of the bottom of equilateral triangle = √ 3 / 2 A
When the angle between the side of an isosceles triangle and the bottom of an isosceles triangle is equal to 0 °, the distance between the side vertex of an isosceles triangle and the third vertex of an isosceles triangle at the bottom = √ 3A - √ 3 / 2 a = √ 3 / 2 A
When the angle between the side of an isosceles triangle and the bottom of an isosceles triangle is equal to 180 degrees, the distance between the side vertex of an isosceles triangle and the third vertex of an isosceles triangle at the bottom = √ 3A + √ 3 / 2 a = 3 √ 3 / 2 A
When the angle between the side of the isosceles triangle and the bottom of the isosceles triangle is greater than 0 ° and less than 180 °, a triangular pyramid can be formed
The value range of the third side length is open (√ 3 / 2 A, 3 √ 3 / 2 a)