Find Rectangle Sides Given Perimeter & Area

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In summary, the conversation discussed finding the lengths of the sides of a rectangle given its perimeter and area. The equations S=2a+2b and P=ab were used to solve for the sides, but the individual solving steps were incorrect. The correct method involved solving for either a or b in one equation and then substituting that value into the other equation. The final result was a=1.2m and b=2.5m. The conversation also mentioned the importance of reviewing pre-calculus material before starting calculus.
  • #1
Government$
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Homework Statement


Find the lengths of the sides of rectangle if perimeter is 7,4 m and area is 3m2.


Homework Equations


S= 2a+2b and P=ab


The Attempt at a Solution


So i tried getting a form P --> a=P/b and then subsstituting in perimeter formula a with P/b ---> S=2P/b+2b but i am stuck here.

Any help would be appreciated. Thank you
 
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  • #2
Government$ said:

Homework Statement


Find the lengths of the sides of rectangle if perimeter is 7,4 m and area is 3m2.


Homework Equations


S= 2a+2b and P=ab


The Attempt at a Solution


So i tried getting a form P --> a=P/b and then subsstituting in perimeter formula a with P/b ---> S=2P/b+2b but i am stuck here.

Any help would be appreciated. Thank you
Start by substituting the given information about the perimeter and area into your two formulas.
 
  • #3
Ok, but still i don't get anywhere:
7,4=a2+b2 and 3m2=ab

7,4=2a+2b---> 7,4=2(a+b)---> a+b=3.7

3=ab---> a=3/b
 
Last edited:
  • #4
Government$ said:
Ok, but still i don't get anywhere:
7,4=a2+b2 and 3m2=ab

The first equation should be written as 2a + 2b = 7.4
The second equation should not have the units in it. ab = 3

Solve either equation for a or b, and then substitute the variable you solved for into the other equation.
 
  • #5
2a+2b=7.4 --> 2a=7.4-2b--> a=7.4/2-2b/2

3=ab---> a=3/b so

3/b=7.4/2-2b/2 Is that what you meant?
 
  • #6
Government$ said:
2a+2b=7.4 --> 2a=7.4-2b--> a=7.4/2-2b/2
Or more simply, a = 3.7 - b

Now substitute 3.7 - b for a in the equation ab = 3.
Government$ said:
3=ab---> a=3/b so

3/b=7.4/2-2b/2 Is that what you meant?
 
  • #7
So a = 3.7 - b then (3.7-b)b=3 --> 3.7b-b^2=3 --> b-b^2=3-3.7 - b-b^2= -0.7 ??

Is that the way or i am wrong and sry if i am boring.

P.S. I have looked at the end of book for result and a=1.2m and b=2.5 but there is no process.
 
  • #8
Government$ said:
So a = 3.7 - b then (3.7-b)b=3 --> 3.7b-b^2=3 --> b-b^2=3-3.7 - b-b^2= -0.7 ??
(3.7-b)b=3 Yes
3.7b-b^2=3 Yes
b-b^2=3-3.7 - b-b^2= -0.7 No

If you subtract 3.7 from 3.7b, you don't get b. 3.7 and 3.7b are not like terms, so can't be added or subtracted to produce something simpler.

The equation 3.7b-b^2=3 is a quadratic equation. Do you know how to solve this type of equation?
Government$ said:
Is that the way or i am wrong and sry if i am boring.

P.S. I have looked at the end of book for result and a=1.2m and b=2.5 but there is no process.
 
  • #9
Mark44 said:
(3.7-b)b=3 Yes
3.7b-b^2=3 Yes
b-b^2=3-3.7 - b-b^2= -0.7 No

If you subtract 3.7 from 3.7b, you don't get b. 3.7 and 3.7b are not like terms, so can't be added or subtracted to produce something simpler.

The equation 3.7b-b^2=3 is a quadratic equation. Do you know how to solve this type of equation?

Thank you very much. I know to solve quadratic equation i just haven't recognized it. Thing is i am doing this for next year during summer break, and title of section is area of geometric body in plain(i don't know if you would call it like that in English language i am translating this from my own language) and i haven't know that they are going to mix it up from last year.

Anyway thanks!
 
  • #10
You mentioned in another post that you will be studying calculus in September. Since you had so many difficulties with this problem, it's good that you are reviewing this material now.

To be honest, though, it is not a good sign that you had so much trouble getting this relatively simple problem started, and you really should not be thinking that 3.7b - 3.7 = b.
 
  • #11
Mark44 said:
You mentioned in another post that you will be studying calculus in September. Since you had so many difficulties with this problem, it's good that you are reviewing this material now.

To be honest, though, it is not a good sign that you had so much trouble getting this relatively simple problem started, and you really should not be thinking that 3.7b - 3.7 = b.

Yes i did, but truth is we still have to do other stuff before calculus like analytical geometry and other stuff. So i don't know if i am starting calculus this year or next i'll be starting third grade in september. And yes i really need to review pre-cal material. Thanks again.
 

1. How do I find the length and width of a rectangle if I know the perimeter and area?

To find the length and width of a rectangle, you can use the following formula: perimeter = 2(length + width) and area = length x width. You can rearrange these equations to solve for the unknown variables, either by substitution or elimination.

2. Can I use the same formula for finding the sides of any rectangle?

Yes, the formula for finding the length and width of a rectangle given the perimeter and area can be used for any rectangle, regardless of its dimensions. It is a universal formula that can be applied to all rectangles.

3. What if I only know the perimeter or the area of the rectangle, can I still find the other side?

Yes, you can still find the other side even if you only know the perimeter or the area. If you only know the perimeter, you can use the formula perimeter = 2(length + width) and solve for the unknown variable. If you only know the area, you can use the formula area = length x width and solve for the unknown variable.

4. Is there a different formula for finding the sides of a square given the perimeter and area?

No, the formula for finding the sides of a square given the perimeter and area is the same as that of a rectangle. This is because a square is a special type of rectangle where all sides are equal in length. Therefore, the same formula applies to both shapes.

5. Can I use this formula to find the sides of other shapes, such as a triangle or circle?

No, this formula is specific to finding the sides of a rectangle given the perimeter and area. Other shapes, such as triangles and circles, have their own formulas for finding the sides or dimensions. It is important to use the correct formula for each specific shape when solving for unknown variables.

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