Respuesta :
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.
[tex]Midsegment=\dfrac{a}{2}[/tex]
The sum of two side is
[tex]a+a=2a[/tex]
Now, the ratio of the length of one midsegment of an equilateral triangle to the sum of two of its side lengths is
[tex]\text{Required ratio}=\dfrac{\text{Length of midsegment}}{\text{sum of two sides}}[/tex]
[tex]\text{Required ratio}=\dfrac{\dfrac{a}{2}}{2a}[/tex]
[tex]\text{Required ratio}=\dfrac{a}{4a}[/tex]
[tex]\text{Required ratio}=\dfrac{1}{4}[/tex]
[tex]\text{Required ratio}=1:4[/tex]
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.
