Given:
One midsegment of an equilateral triangle.
To find:
The ratio of the length of one midsegment of an equilateral triangle to the sum of two of its side lengths.
Solution:
All sides of an equilateral triangle are same.
Let a be the each side of the equilateral triangle.
Length of the midsegment is equal to the half of the non included side or third side.
The sum of two side is
Now, the ratio of the length of one midsegment of an equilateral triangle to the sum of two of its side lengths is
Therefore, the ratio of the length of one midsegment of an equilateral triangle to the sum of two of its side lengths is 1:4.