PLEASE HELP GEOMETRY QUESTION

The perimeter of an equilateral triangle is 12\/3 cm. Find the radius, apothem and area of the equilateral triangle.

Irina-Kira [14]

Answer:

Radius - 4

Apothem - 2

Area - $12\sqrt{3}$ or 20.8

Step-by-step explanation:

Try to draw out my explanation so you know what this looks like.

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This is an equilateral triangle, so all sides are the same length. The perimeter can be divided by 3 to get each side length...

$12\sqrt{3} \div3 = 4\sqrt{3}$

Now that we know the side lengths, we can get this started!

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Now, an equilateral triangle has angles that all equal 60 degrees. We can bisect this into TWO special case triangles of measures 90-60-30.

4 times the square root of 3 will be the hypotenuse, and the smallest leg is always half of that. The larger leg is represented as the small leg times the square root of 3.

$Small=2\sqrt{3} \\Hypotenuse = 4\sqrt{3} \\Long =6$

By the way, the formula for the area can be either of the two:

$A= \frac{1}{2} bh\\or\\A = \frac{1}{2} NAS$

we can easily find the area using the first formula.

$A= \frac{1}{2} (4\sqrt{3} )(6)\\A=12\sqrt{3}$

The radius is the distance from the center to the corners & the apothem is the distance from the center to a side...

So we can divide the big triangle into a mini triangle at the bottom left/right

The height (small leg) of that triangle would be the apothem

The hypotenuse of that triangle would be the radius.

I did the math really quick because this is getting long. Anyhow, the small leg is 2 so is the apothem, and the hypotenus is 4, so is the radius

Happy April Fool's btw, lol.

4 0

3 years ago

Slope 9/5 and this line is passing through ( 0,5)

Law Incorporation [45]

Answer:

uuuujjjjj

Step-by-step explanation:

nnnnnnnnnnnnnñbbbbbbb

4 0

3 years ago

To do so, the research has 100 high school students complete the maze with classical music playing. The mean time for these stud

Marizza181 [45]

Answer:

test statistic, z = −1.74

Step-by-step explanation:

given data

students n = 100

mean time x = 41.13 seconds

σ = 5

we consider µ = 42

solution

we get here The test statistic that is express as

test statistic, z = $\frac{x-\mu }{\frac{\sigma }{\sqrt{n}}}$ ......................1

put here value and we will get

test statistic, z = \frac{41.13-42}{\frac{5 }{\sqrt{100}}}

test statistic, z = −1.74

8 0

3 years ago

A baseball player has a batting average of 0.25. What is the probability that he has exactly 2 hits in his next 7 at bats

marissa [1.9K]

Answer:

The probability that he has exactly 2 hits in his next 7 at-bats is 0.3115.

Step-by-step explanation:

We are given that a baseball player has a batting average of 0.25 and we have to find the probability that he has exactly 2 hits in his next 7 at-bats.

Let X = Number of hits made by a baseball player

The above situation can be represented through binomial distribution;

$P(X = r) = \binom{n}{r}\times p^{r} \times (1-p)^{n-r}; x = 0,1,2,......$