Math, asked by sarthak28jan, 3 months ago

A wire is in the shape of a rectangle. Its length is 36cm and
breadth is 32cm. If the same wire is bent in the shape of a
square, what will be the measure of each side? Also find
which shape encloses more area?

Answers

Answered by navnoor375
4

Step-by-step explanation:

area of rectangle = length and width

= 36*32

=1152 cm2

Area of square = side *side

let side of square be x

x*x =1152

x2 = 1152 cm2

Answered by Anonymous
8

\tt \pink{Given}\begin{cases}&\sf{Length\:of\:the\:rectangle=\bf{36\:cm.}} \\ \\ &\sf{Breadth\:of\:the\:rectangle=\bf{32\:cm.}}\end{cases} \\

To FinD:-

  • Measure of each side of square.
  • Shape that encloses more area.

SolutioN:-

We know that,

\normalsize\quad{\purple{\underline{\boxed{\sf{Perimeter_{(rectangle)}=2(Length+Breadth)}}}}}

\tt {Here}\begin{cases}&\sf{Length=\bf{36\:cm}} \\ \\ &\sf{Breadth=\bf{32\:cm}}\end{cases} \\ \\

  • Putting the values,

 \\ :\normalsize\implies{\sf{Perimeter_{(Rectangle)}=2(36+32)}} \\

 \\ \qquad:\normalsize\implies{\sf{Perimeter_{(Rectangle)}=2\times68}} \\

 \\ \qquad\quad\quad\normalsize\therefore\boxed{\mathfrak{\pink{Perimeter_{Rectangle)}=136\:cm.}}} \\

Now,

  • It is said that the wire is bent in the shape of a square.

 \\ \ \ \ \ \ \normalsize{\sf{\pink{\underline{Perimeter_{(Rectangle)}=Perimeter_{(square)}}}}} \\ \\

We know that,

\normalsize\qquad\quad{\purple{\underline{\boxed{\sf{Perimeter_{(square)}=4\times side}}}}}

\tt {Here}\begin{cases}&\sf{Perimeter_{(square)}=\bf{136\:cm}} \\ \\ &\sf{Side=\bf{?}}\end{cases} \\ \\

  • Putting the values,

 \\ :\normalsize\implies{\sf{136=4\times side}} \\

 \\ \qquad:\normalsize\implies{\sf{\dfrac{136}{4}=side}} \\

 \\ \qquad\quad:\normalsize\implies{\sf{\cancel{\dfrac{136}{4}}=side}} \\

 \\ \qquad\quad\quad\normalsize\therefore\boxed{\mathfrak{\pink{Side_{(square)}=34\:cm.}}} \\

____________________________________

Area of rectangle :

We know that,

\normalsize\qquad\quad{\purple{\underline{\boxed{\sf{Area_{(rectangle)}=Length\times Breadth}}}}}

\tt {Here}\begin{cases}&\sf{Length=\bf{36\:cm}} \\ \\ &\sf{Breadth=\bf{32\:cm}}\end{cases} \\ \\

  • Putting the values,

 \\ :\normalsize\implies{\sf{Area_{(Rectangle)}=36\times32}} \\

 \\ \qquad\quad\quad\normalsize\therefore\boxed{\mathfrak{\pink{Area_{(Rectangle)}=1152\:cm^2.}}} \\ \\

Area of square :

We know that,

\normalsize\qquad\quad{\purple{\underline{\boxed{\sf{Area_{(square)}=side\times side}}}}}

\tt {Here}\begin{cases}&\sf{Side=\bf{34\:cm}}\end{cases} \\ \\

  • Putting the values,

 \\ :\normalsize\implies{\sf{Area_{(square)}=34\times34}} \\

 \\ \qquad\quad\quad\normalsize\therefore\boxed{\mathfrak{\pink{Area_{(square)}=1156\:cm^2.}}} \\ \\

By comparing the area of both rectangle and square,

  • Square encloses more area.

_______________________________________

  • Measure of each side of square is 34 cm.
  • Square encloses more area.
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