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

Mathematics

1 answer:

mars1129 [50]3 years ago

3 0

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.

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Answer:

Option A is the correct choice.

Step-by-step explanation:

Let d be the number of boxes of duck calls and t be the number of boxes of turkey calls.

We have been given that a company sells boxes of duck calls for $35 and boxes of turkey calls (t) for $45, so the revenue earned from selling d boxes of duck and t boxes of turkey call will be 35d and 45t respectively.

Further, the company plan to make $300. We can represent this information as:

$35d+45t=300...(1)$

We are also told that they make batches of duck calls that fill 6 boxes and batches of turkey calls that fill 8 boxes. the company only has 42 boxes. We can represent this information as:

$6d+8t=42...(2)$