One Geometry question help please

[Nikkimarie]

Hi! I was doing this math problem (number 5) and I am so confused by what I did wrong. I know I didn’t do it right if someone could help that would be amazing!

 

[lev888]

Hi! I was doing this math problem (number 5) and I am so confused by what I did wrong. I know I didn’t do it right if someone could help that would be amazing!

What does the overall perimeter consist of? How do we find the lengths of all the components?

 

[Deleted member 4993]

Hi! I was doing this math problem (number 5) and I am so confused by what I did wrong. I know I didn’t do it right if someone could help that would be amazing!

I think this problem is missing some information.

According my interpretation (assuming 4 quarter circles of radius 'r' has been cut out from the rectangle)

Perimeter = 2 * [6 + (6 +2r)] - 4 * 2 * r + 4 * (2 * π * r / 4) = 24 + r * ( 2 * π - 4)

Without measurement for 'r' - it cannot be done.

 

[Nikkimarie]

What does the overall perimeter consist of? How do we find the lengths of all the components?

The perimeter consists of inches and 90° angles so four angles of 90. That is one circle and then it has two sides of 6 inches but other the. That I am lost

 

[Nikkimarie]

View attachment 18627

I think this problem is missing some information.

According my interpretation (assuming 4 quarter circles of radius 'r' has been cut out from the rectangle)

Perimeter = 2 * [6 + (6 +2r)] - 4 * 2 * r + 4 * (2 * π * r / 4) = 24 + r * ( 2 * π - 4)

Without measurement for 'r' - it cannot be done.

Wouldnt R be 90° and four 90° wouldn’t it then be 360? So one whole circle out of the equation?

 

[Nikkimarie]

View attachment 18627

I think this problem is missing some information.

According my interpretation (assuming 4 quarter circles of radius 'r' has been cut out from the rectangle)

Perimeter = 2 * [6 + (6 +2r)] - 4 * 2 * r + 4 * (2 * π * r / 4) = 24 + r * ( 2 * π - 4)

Without measurement for 'r' - it cannot be done.

Also what if I put it in terms of pi and then converted PI to Inches?

 

[lev888]

Wouldnt R be 90° and four 90° wouldn’t it then be 360? So one whole circle out of the equation?

R is radius of the circle used to make 4 cut outs, it's distance, measured in inches. 90° is an angle of the rectangle, measured in degrees.

 

[Nikkimarie]

R is radius of the circle used to make 4 cut outs, it's distance, measured in inches. 90° is an angle of the rectangle, measured in degrees.

What if since two sides of the Square are 6” and with including the circle cuts the other side is also 6’ and since each circle part is the same size they would be 2 inches each? If that makes any sense

 

[Nikkimarie]

R is radius of the circle used to make 4 cut outs, it's distance, measured in inches. 90° is an angle of the rectangle, measured in degrees.

I retried it and I got this

 

[lev888]

What if since two sides of the Square are 6” and with including the circle cuts the other side is also 6’ and since each circle part is the same size they would be 2 inches each? If that makes any sense

I don't follow. Where do you see a square? How did you get 2 inches?
First of all, it does look like there is missing info - without knowing the radius I don't see how to solve it.
In any case, forget for a moment about numbers. Can you answer my first question?

 

[Nikkimarie]

Y

I don't follow. Where do you see a square? How did you get 2 inches?
First of all, it does look like there is missing info - without knowing the radius I don't see how to solve it.
In any case, forget for a moment about numbers. Can you answer my first question?

yes sorry, the square the shape. Forget about the circle quarters and imagine them filled in. That is a square because of the information given. And the perimeter consist of two 6” sides and then 2 unknown sides but if you fill it in with the circles it’s then four 6” sides

 

[pka]

You have four \(90^o\) arcs. The centre of each would have been a vertex of a rectangle.
What would be the dimensions of that rectangle ? What is the radius of the arcs?
Do the four congruent arcs compost a circle?

 

[Nikkimarie]

You have four \(90^o\) arcs. The centre of each would have been a vertex of a rectangle.
What would be the dimensions of that rectangle ? What is the radius of the arcs?
Do the four congruent arcs compost a circle?

The dimensions of the rectangle I do not know but the radius of the circle I believe is 1 inch. The four arcs equal one circle yes

 

[Nikkimarie]

Y

yes sorry, the square the shape. Forget about the circle quarters and imagine them filled in. That is a square because of the information given. And the perimeter consist of two 6” sides and then 2 unknown sides but if you fill it in with the circles it’s then four 6” sides

I cross multiplied using the arch length and I believe the radius is 1

 

[lev888]

Y

yes sorry, the square the shape. Forget about the circle quarters and imagine them filled in. That is a square because of the information given. And the perimeter consist of two 6” sides and then 2 unknown sides but if you fill it in with the circles it’s then four 6” sides

I don't see a square! I see a rectangle. Its height is 6in. Its length is unknown.
What I wanted you to say: the perimeter consists of lengths of 4 straight segments and 4 arcs. Do you see it?
Now, back to numbers.
2 of the (horizontal) segments are 6in.
2 vertical segments ?
Arc length = ? What's the formula?

 

[Nikkimarie]

I don't see a square! I see a rectangle. Its height is 6in. Its length is unknown.
What I wanted you to say: the perimeter consists of lengths of 4 straight segments and 4 arcs. Do you see it?
Now, back to numbers.
2 of the (horizontal) segments are 6in.
2 vertical segments ?
Arc length = ? What's the formula?

The arch length I believe is 0.5 as seen in my attachment. Yes I see what you are saying with the perimeter sorry about that. I believe the radius is 1 inch aswel

 

[lev888]

The arch length I believe is 0.5 as seen in my attachment. Yes I see what you are saying with the perimeter sorry about that. I believe the radius is 1 inch aswel

Why is radius 1? What's the formula for arc length?

 

[pka]

The arch length I believe is 0.5 as seen in my attachment. Yes I see what you are saying with the perimeter sorry about that. I believe the radius is 1 inch aswel

A circle with \(1\) has a circumference of \(2\pi\). What is one fourth of that?

 

[Nikkimarie]

Why is radius 1? What's the formula for arc length?

And I believe the radius is 1 because using this formula the circumference is 2

 

[Nikkimarie]

A circle with \(1\) has a circumference of \(2\pi\). What is one fourth of that?

0.5!