Question

A wire is in the shape of a square of side 10 cm. If the wire is rebent into a rectangle of length 12 cm, find its breadth. Which encloses more area, the square or the rectangle?​

Answer 1

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Answer 2

Given:-

• Side of Square = 10cm
• Length of Square = 20cm

To Find:-

• Breadth
• Which Encloses More, Square or Rectangle.

Solution with Step by Step Explanation:-

Side of the Square = 10cm

Length of The wire =

Perimeter of the Square = 4 × side

= 4 × 10cm

= 40cm

Length of The Rectangle = 12cm,

Let B to be Breadth of the Rectangle .

Perimeter of Rectangle = 2 × ( L + B )

= 40 = 2 × ( L + B )

= $\dfrac{40}{2}$ = 12 + b

b = 20 - 12 = 8cm

Therefore,

The Breadth of the Rectangle is 8 cm

Area of the Square = (side)²

= 10cm × 10cm

= 100cm²

Area of The Rectangle = ${ l × b }$

= 12cm × 8cm

= 96cm²

So, The square encloses more area even though its Perimeter is the same as that of the rectangle .