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.

$Midsegment=\dfrac{a}{2}$

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

$\text{Required ratio}=\dfrac{\text{Length of midsegment}}{\text{sum of two sides}}$

$\text{Required ratio}=\dfrac{\dfrac{a}{2}}{2a}$

$\text{Required ratio}=\dfrac{a}{4a}$

$\text{Required ratio}=\dfrac{1}{4}$

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

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.