Question

A wire is in the shape of a square of side \[8cm\]. If the wire is rebent into a rectangle of length \[10cm,\] find its breadth. Which of the two shapes encloses a larger area?

Answer 1

Hint: Here, the same wire is used to make rectangle and square. So, the perimeter of both will be the same. Also, to find the area of the rectangle, we require breadth. To


Complete step by step solution:
\[\left[ {We{\text{ }}need{\text{ }}to{\text{ }}find{\text{ }}breadth{\text{ }} = {\text{ }}b} \right]\]
According to the question:
Perimeter of square = Perimeter of rectangle.
Formula of perimeter of square $ = 4a$
where $a$ is the side of a square$ = 4a$
Formula of perimeter of a rectangle$ = 2(l + b)$.
where $l$ is the length of a rectangle and $b$ is the breadth of a rectangle.
so now we have to compare $
   = 2(l + b) \\
    \\
    \\
 $ perimeter of a square with Formula of perimeter of a rectangle
$
  4a = 2(l + b) \\
  4 \times 8 = 2(10 + b) \\
  32 = 20 + 2b \\
  2b = 32 - 20 \\
  b = \dfrac{{12}}{2} = 6cm \\
$
Area of square = ${a^2} = {(8)^2} = 64c{m^2}$
Area of rectangle = $l \times b = 6 \times 10 = 60c{m^2}$
Therefore, square encloses more area = $64c{m^2}$


Note: The area of rectangle and square formula must be learnt along with the perimeter formula.Appropriate formulas should be used at the right places in the solution