Question

What is the ratio of the length of one midsegment of an equilateral triangle to the sum of two of its side lengths?

Answer 1

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.

`Midsegment=(a)/(2)`

The sum of two side is

`a+a=2a`

Now, the ratio of the length of one midsegment of an equilateral triangle to the sum of two of its side lengths is

`\text{Required ratio}=\frac{\text{Length of midsegment}}{\text{sum of two sides}}`

`\text{Required ratio}=((a)/(2))/(2a)`

`\text{Required ratio}=(a)/(4a)`

`\text{Required ratio}=(1)/(4)`

`\text{Required ratio}=1:4`

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.