Solve Polygon Problem: 1:2 Ratio & 3:4 Sum

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In summary, the problem involves finding the number of sides in two regular polygons with a given ratio between their number of sides and a given ratio between the sum of their interior angles. The solution provided in the conversation results in -1 and -2 sides, while the book's answer is 5 and 10 sides, but this answer does not match the given ratios. Further clarification is needed to determine the correct answer.
  • #1
1/2"
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polygon problem (?!)

Hi there!:smile:
I have got an problem here.It's a simple one.Not much to think about
"The ratio between the numbers of sides of two regular polygons is 1:2 and the ratio between the sum of their 3:4.Find the number of sides in each polygon"
It appears easy and is too. but the problem is the answer i am getting is absolutely weird ie.,
-1 and -2 sides .:uhh:
In the work out I had considered the no . of sides to be x and 2x
the sum of interior angles 3y and 4y respectively.
so it ends up as {(4x-4)*90} -{(2x-4)*90} =4y-3y
=>180x=y
so i sustituted it in the equation (2x-4)*90=3y which ends up as -4=4x .: x= -1:eek::uhh::
Book's answers are polygon with 5 and 10 sides .
I don't know whether I have gone wrong some where:confused:. If so Please help me correct it!(If the book's answer is wrong mention that too :smile:!)
Thank you
 
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  • #2
Hi 1/2"! :smile:
1/2" said:
"The ratio between the numbers of sides of two regular polygons is 1:2 and the ratio between the sum of their 3:4.Find the number of sides in each polygon"

If you mean "the ratio between the sum of their interior angles is 3:4", then I agree, the solution is -1 and -2 ! :biggrin:

A solution of 5 and 10 would have a ratio of 3:8, not 3:4.
 
  • #3


Thanks tiny-tim.
 

1. What is a 1:2 ratio and 3:4 sum in relation to a polygon problem?

A 1:2 ratio means that the first quantity is half of the second quantity. In the context of a polygon problem, this could refer to the ratio of the lengths of two sides of a polygon. A 3:4 sum refers to the sum of three quantities being equal to four times the fourth quantity. In a polygon problem, this could refer to the sum of the angles in a quadrilateral being three times the fourth angle.

2. How do you solve a polygon problem with a 1:2 ratio and 3:4 sum?

To solve a polygon problem with a 1:2 ratio and 3:4 sum, you would need to set up an equation based on the given information and use algebraic methods to solve for the unknown quantities. This could involve using the properties of polygons, such as the sum of angles in a polygon being equal to 180 degrees, to set up equations.

3. Can a polygon have a 1:2 ratio and 3:4 sum for all of its sides and angles?

Yes, it is possible for a polygon to have a 1:2 ratio and 3:4 sum for all of its sides and angles. This would depend on the specific measurements and properties of the polygon, and may require more complex calculations to determine.

4. Are there any real-world applications for solving polygon problems with a 1:2 ratio and 3:4 sum?

Yes, there are many real-world applications for solving polygon problems with a 1:2 ratio and 3:4 sum. For example, architects and engineers may use these types of problems to design and construct buildings with specific proportions and angles. These types of problems can also be used in geometry and trigonometry to solve for unknown measurements and angles in various shapes and structures.

5. What other types of ratios and sums can be used to solve polygon problems?

There are many other types of ratios and sums that can be used to solve polygon problems, depending on the given information and the specific properties of the polygon. For example, a common ratio used in polygon problems is the 1:1 ratio, which refers to two quantities being equal in size. Sums can also vary, such as a 2:3 sum or a 5:7 sum. The key is to carefully analyze the given information and use mathematical principles to set up and solve equations.

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