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Nina [5.8K]
3 years ago
15

The sides of two regular octagons are 3 in. And 6 in. respectively. Find the ratio of their perimeters and their areas

Mathematics
1 answer:
photoshop1234 [79]3 years ago
6 0

The ratio of their perimeters is \frac{1}{2} and the ratio of their areas is \frac{1}{4}

Step-by-step explanation:

A regular n-side polygon has

  • n equal sides
  • n equal angles
  • The measure of each interior angle = \frac{(n-2).180}{n}
  • Its perimeter = n × a, where a is the length of its side

<em>V.I.Note: all regular polygons have same number of sides are similar, because their interior angles are equal in measures and their sides are proportion</em>

<em />

∵ There are to regular octagons

- Regular octagon has 8 equal sides and 8 equal angles

∴ The two octagon are similar

∵ Their sides are 3 inches and 6 inches

∴ The constant ratio between their sides = \frac{3}{6}

- Divide the two terms of the ratio by 3 to simplify it

∴ The constant ratio between their sides = \frac{1}{2}

In similar figures <em>the ratio between their perimeters is equal to the constant ratio between their sides</em>, and <em>the ratio between their areas is equal to square the constant ratio between their sides</em>

∵ The two octagons are similar

∵ The constant ratio between their sides = \frac{1}{2}

∵ The ratio between their perimeters = the constant ratio between

   their sides

∴ The ratio between their perimeters = \frac{1}{2}

∵ The ratio between their areas = (constant ratio)²

∴ The ratio between their areas = (\frac{1}{2})^{2}=\frac{1}{4}

The ratio of their perimeters is \frac{1}{2} and the ratio of their areas is \frac{1}{4}

Learn more:

You can learn more about the polygons in brainly.com/question/3779181

#LearnwithBrainly

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Pavlova-9 [17]
For this one you can use 3/8 + 3/8 since 3+3 is equals to 6 and the 8 stays as it is.
I hope this helps.
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3 years ago
What is the slope of a line parallel 18x+15y=90
luda_lava [24]

Answer:

-6/5

Step-by-step explanation:

Get y by itself to get the slope. So 18x+15y=90. Move 18x to the other side of the equation. Now you have 15y=-18x+90. Divide both sides by 15 to get y by itself. Now it's y= -18/15x + 6. Reduce -18/15 to the simplest fraction. You have y= -6/5x+6. Any number can replace the 6 in the equation to give you a parallel line...it's the slope that makes it parallel, not the y intercept. So y= -6/5x+10 or y=- -6/5x-1 would satisfy your parallel slope equation.

5 0
2 years ago
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What is the value of cosine (StartFraction 4 pi Over 3 EndFraction)? cos(4pi/3)
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8 0
2 years ago
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What is x^2+11x=0? im confused on what my “c value” is.
jeka94

Answer:

c=0

Step-by-step explanation:

x² + 11x + 0 = y

x² + 11x + 0 = 0

U already know that y=0 by looking at the equations above,

But your worksheet never state "c", so we will take that c is 0   (look at the equations above.)

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7 0
2 years ago
What is 4(4m-3)-(m-5)=52 step by step
ch4aika [34]

Answer:

-3

Step-by-step explanation:

Simplifying

4(4m + -3) + -1(m + -5) = -52

Reorder the terms:

4(-3 + 4m) + -1(m + -5) = -52

(-3 * 4 + 4m * 4) + -1(m + -5) = -52

(-12 + 16m) + -1(m + -5) = -52

Reorder the terms:

-12 + 16m + -1(-5 + m) = -52

-12 + 16m + (-5 * -1 + m * -1) = -52

-12 + 16m + (5 + -1m) = -52

Reorder the terms:

-12 + 5 + 16m + -1m = -52

Combine like terms: -12 + 5 = -7

-7 + 16m + -1m = -52

Combine like terms: 16m + -1m = 15m

-7 + 15m = -52

Solving

-7 + 15m = -52

Solving for variable 'm'.

Move all terms containing m to the left, all other terms to the right.

Add '7' to each side of the equation.

-7 + 7 + 15m = -52 + 7

Combine like terms: -7 + 7 = 0

0 + 15m = -52 + 7

15m = -52 + 7

Combine like terms: -52 + 7 = -45

15m = -45

Divide each side by '15'.

m = -3

Simplifying

m = -3

Hope this helped :)

8 0
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