What is the least ten digit whole number

The perimeter of equilateral triangle ABC is 81/3 centimeters, find the length of the radius and apothem.

MAXImum [283]

There is a typo error, the perimeter of equilateral triangle ABC is 81/√3 centimeters.

Answer:

Radius = OB= 27 cm

Apothem = 13.5 cm

A diagram is attached for reference.

Step-by-step explanation:

Given,

The perimeter of equilateral triangle ABC is 81/√3 centimeters.

Substituting this in the formula of perimeter of equilateral triangle = $3\times\ side$

$3\times\ side$ $=[tex]81\sqrt{3}$

$Side = \frac{81\sqrt{3} }{3} =27\sqrt{3} \ cm$

Thus from the diagram , Side $AB=BC=AC= 27\sqrt{3} \ cm$

We know each angle of an equilateral triangle is 60°.

From the diagram, OB is an angle bisector.

Thus $\angle OBC = 30$ °

Apothem is the line segment from the mid point of any side to the center the equilateral triangle.

Therefore considering ΔOBE, and applying tan function.

$tan\theta =\frac{perpendicular}{base} \\tan\theta=\frac{OE}{BE} \\tan\theta=\frac{OE}{\frac{27\sqrt{3}}{2} } \\tan30\times {\frac{27\sqrt{3} }{2} }= OE\\\frac{1}{\sqrt{3} } \times\frac{27\sqrt{3} }{2} =OE\\$

Thus ,apothem OE= 13.5 cm

Now for radius,

We consider ΔOBE

$cos\theta=\frac{base}{hypotenuse} \\cos30= \frac{BE}{OB} \\Cos30 = \frac{\frac{27\sqrt{3} }{2}}{OB} \\OB= \frac{\frac{27\sqrt{3} }{2}}{cos30} \\OB= \frac{\frac{27\sqrt{3} }{2}}{\frac{\sqrt{3} }{2} } \\OB =27 \ cm$

Thus for

Perimeter of equilateral triangle ABC is 81/√3 centimeters,

The radius of equilateral triangle ABC is 27 cm

The apothem of equilateral triangle ABC is 13.5 cm

4 0

2 years ago

Find the value of two numbers is their sum is 21 and their difference is 3

kobusy [5.1K]

Hello from MrBillDoesMath

Answer: 12, 9

Discussion:

Let x be the first number and y the second number. The form the problem statement:

x + y = 21

x - y = 3

Add the two equations. This gives:

(x + x ) + ( y-y) = 21 + 3 =>

2x + 0 = 24 =>

x = 12

Since x -y =3, substituting in the value of x gives, 12 - y = 3 so y = 9

Thank you,

Mr. B

8 0

2 years ago

Read 2 more answers

Select all the numbers that show 1/2% as an equivalent fraction, decimal, or percent.

ipn [44]

0.5% is the answer hope this helps

3 0

2 years ago

The perimeter of an equilateral triangle is p and the length of a side is s.

kompoz [17]

Answer:

s=7

p=3s

Step-by-step explanation:

The perimeter is the side length times 3

So the equation would be p=3s

Plug in 21 for p

21=3s

That means s=7

8 0

2 years ago

The fence is 106 meters long. Each section of fence is 3 meters long. How many sections were needed to complete the fence?

denis23 [38]

Answer: approximately 35
explanation:
divide 106 by 3 = 35.33

4 0

2 years ago