Question

A wire is bent to form a square of side 30 cm. If the wire is rebent to form a rectangle of length 7 cm. find the breadth of the rectangle.

Answer 1

Given thαt,

• A wire is bent to form a square of side 30 cm.
• The wire is rebent to form a rectangle of length 7cm.

◾️We need to find the breadth of rectangle.

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To do so, see how to solve! :D

As the wire is same so it's length(perimeter) must be the same. Therefore, we will find the perimeter of square and then we assume breadth to be B. and put the perimeter in equal to the perimeter of rectangle.

Formulaes to be used :

$\large{\boxed{\sf{\orange{perimeter_{(square)} = 4a,\:where\:a\:=\:side}}}}$

$\large{\boxed{\sf{\orange{perimeter_{(rectangle)} = 2(l+b),\:where\:l\:=\:side\:and\:b=\:breadth}}}}$

So let's start!

Let the breadth be B.

• Substitute the values in the formulae of perimeter of square!

:$\implies{\sf{4a=4(30)}}$

:$\implies{\sf{120}}$

• Substitute the values in the formulae of perimeter of rectangle and put 120 in its equal.

:$\implies{\sf{2(7+B) = 120}}$

• Simplify this.

:$\implies{\sf{14+2B = 120}}$

:$\implies{\sf{2B = 120-14}}$

:$\implies{\sf{2B = 106}}$

:$\implies{\sf{B = \dfrac{106}{2}}}$

:$\large\implies{\boxed{\sf{\red{B = 53}}}}$

Therefore, the breadth of the rectangle is 53 respectively.

And we are done! ✔

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Answer 2

$\LARGE{\color{t}{\textsf{\textbf {\underline {\underline{ Anѕwєr : }}}}}}$

ᎶᎥ۷ꫀꪀ :

• Ꭺ ωᎥɾꫀ Ꭵs bꫀꪀt tꪮ fꪮɾm ɑ ઽquaɾꫀ ꪮf ઽᎥժꫀ 30 ᥴm.
• Ƭhꫀ ωᎥɾꫀ is ɾꫀbꫀꪀt tꪮ fꪮɾm a ɾꫀᥴtɑꪀᧁlꫀ ꪮf lꫀꪀᧁth 7ᥴm.

Ƭꪮ ŦᎥꪀძ :

• βrꫀaძtհ ꪮŦ ɾꫀᥴtɑꪀᧁlꫀ.

Ꮯꪮꪀᥴꫀρt :

• As the wire is same so it's length(perimeter) must be the same. Therefore, we will find the perimeter of square and then we assume breadth to be B. and put the perimeter in equal to the perimeter of rectangle.

Fꪮɾʍυlɑꫀs tꪮ ҍꫀ υઽꫀժ :

$\large{{\sf \pmb {\red{{ᏢꫀɾᎥʍꫀtꫀɾ_{(ઽҩuɑɾe)} = 4ɑ,\:աhꫀɾꫀ\:ɑ\:=\:ઽᎥժꫀ}}}}}$

$\large{{\sf \pmb{{\purple{ᏢꫀɾᎥʍꫀtꫀɾ_{(ɾꫀᥴtɑꪀᧁlꫀ)} = 2(l+b),\:աhꫀɾꫀ\:l \:=\:sᎥժꫀ\:ɑꪀժ\:b=\:bꫀɑժth}}}}}$

ᏕꪮlυtᎥꪮꪀ :

• Let the breadth be B.

Substitute the values in the formulae of perimeter of square!

$:\ \pink \implies{\sf{4a=4(30)}}$

$: \pink\implies{\sf{120}}$

Substitute the values in the formulae of perimeter of rectangle and put 120 in its equal.

$: \pink\implies{\sf{2(7+B) = 120}}$

ᏕᎥʍρӀᎥŦყ ᴛʜᎥઽ :

$: \pink\implies{\sf{14+2B = 120}}$

$: \pink\implies{\sf{2B = 120-14}}$

$: \pink\implies{\sf{2B = 106}}$

$: \pink\implies{\sf{B = \dfrac{106}{2}}}$

$: \large \pink\implies{\boxed{\sf \pmb {\underline{{\blue{B = 53}}}}}}$

Thꫀrꫀfꪮrꫀ,

Ƭʜꫀ bгꫀɑժᴛʜ ꪮŦ ᴛʜꫀ гꫀᥴᴛɑꪀᧁlꫀ ઽs 53 гꫀઽρꫀᥴᴛᎥvꫀlყ.

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