(22) A wire is in the shape of side 12 cm, if the wire is rebent into a rectangle of length 14 cm, find its breadth. Which encloses more area, the square the rectangle?
Answers
Answer :
- Area of square is greater by 4cm²
Given :
- A wire is in the shape of side is 12cm
- The wire is rebent into a rectangle of length 14cm
To find :
- Breadth
- which figure encloses more area
Solution :
Given that ,
- Side of a square = 12cm
As we know that,
- Perimeter of square = 4 × s
》4 × 12 = 48cm
Hence, Perimeter of square is 48cm
Now ,
- Perimeter of square = Perimeter of rectangle
As we know that,
- Perimeter of rectangle = 2(length + breadth)
》2(l + b) = 48
》2(14 + b) = 48
》(14 + b) = 48/2
》14 + b = 24
》b = 24 - 14
》b = 10cm
Hence , Breadth of rectangle is 10cm
Now we have to find the which figure encloses more area :
- Area of square = (side)² = 12 × 12 = 144cm²
- Area of rectangle = length × breadth = 14 × 10 = 140cm²
》144 - 140 = 4
Hence , Area of square is greater by 4cm²
Answer:
GivEn:
Side of Square = 10 cm
Length of Rectangle = 12 cm
⠀⠀⠀⠀⠀⠀⠀
To find:
Which encloses more area, the square or the rectangle?
⠀⠀⠀⠀⠀⠀⠀
Solution:
⠀⠀⠀⠀
A wire of Square shape is rebent into Rectanglular shape.
⠀⠀⠀⠀⠀⠀⠀
We have,
Side of Square = 10 cm
⠀⠀⠀⠀⠀⠀⠀
We know that,
⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀
Given that,
Length of Rectangle = 12 cm
Let breadth of Rectangle be b.
⠀⠀⠀⠀⠀⠀⠀
Perimeter of square = Perimeter of Rectangle = 40 cm
⠀⠀⠀⠀⠀⠀⠀
We know that,
⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀
━━━━━━━━━━━━━━━
We know that,
⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀
☯ Therefore, Area enclosed by the square,
⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀
━━━━━━━━━━━━━━━
We know that,
⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀
☯ Therefore, Area enclosed by the square,
⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀
☯ Thus, The Difference in their area,
⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀
Hence, The square encloses more area by 4 cm².