34. A wire is in the shape of a square of side 15cm . If the wire is rebent
into a rectangle of length 18cm , find it's breadth. Which encloses
more Area , the square or the rectangle and by how much .
Answers
Given data :
- A wire is in the shape of a square of side 15 cm.
- If the wire is rebent into a rectangle of length 18 cm.
To find : Breadth of rectangle, and which encloses more area, the square or the rectangle and by how much ?
Solution : Here, according to given data,
⟹ side of square = 15 cm
⟹ length of rectangle ( L ) = 18 cm
⟹ breadth of rectangle ( B ) = ?
We know that, wire is rebent into a rectangle. Hence perimeter of square is equal to permeter of rectangle.
⟹ perimeter of square = permeter of rectangle.
⟹ 4 * side = 2 ( L + B )
⟹ 4 * 15 = 2 ( 18 + B )
⟹ 60 = 36 + 2B
⟹ 60 - 36 = 2B
⟹ 24 = 2B i.e.
⟹ B = 24/2
⟹ B = 12 cm
Hence, breadth of the rectangle is 12 cm.
Now,
⟹ Area of square = ( side )²
⟹ Area of square = ( 15 )²
⟹ Area of square = 225 cm² ....( 1 )
Now,
⟹ Area of rectangle = L * B
⟹ Area of rectangle = 18 * 12
⟹ Area of rectangle = 216 cm² ....( 2 )
Now, by comparing eq. ( 1 ) & eq. ( 2 )
We know that, area of the square is greater than area of the rectangle.
⟹ Area of square - Area of rectangle
⟹ 225 - 216
⟹ 9 cm²
Therefore area of the square is greater than area of the rectangle by 9 cm².
Answer :
- Breadth of the rectangle is 12 cm.
- Area of the square is greater than area of the rectangle by 9 cm².
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