Question

A wire is in the shape of a square of side 10cm. if the wire is rebent into a rectangle of length 12cm, find its breadth.which figure encloses more area and by how much?

Answer 1

${ \huge{ \bold{ \underline{ \underline{ \red{Question:-}}}}}}$

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

_______________

${ \huge{ \bold{ \underline{ \underline{ \orange{Answer:-}}}}}}$

✒Given : -

• A wire is in the shape of a square of side 10cm. The wire is rebent into a rectangle of length 12cm..

✒To Find : -

• Breadth and Which figure encloses more area and by how much ?

✒Formula Used : -

$\leadsto\sf{{ \small{ \bold{ \bold{ \bold{ \purple{Perimeter\:of\:Square=4\times{Side}}}}}}}}$

$\dashrightarrow\sf{4\times{Side}}$

$\dashrightarrow\sf{4\times{10cm}}$

$\dashrightarrow\sf\bold{40cm}$

☛As we know that : -

• Length of the rectangle = 12cm

✒So ,

$\dashrightarrow\sf{Perimeter\:of\:the\:rectangle=Length\:of\:wire=40cm}$

✒Formula Used : -

$\leadsto\sf{{ \small{ \bold{ \bold{ \bold{ \purple{Perimeter\:of\:rectangle=2(l+b)}}}}}}}$

➦On Substituting Values : -

$\dashrightarrow\sf{40=2(12+b)}$

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

$\dashrightarrow\sf{b=20-12}$

$\leadsto\sf{{ \large{ \boxed{ \bold{ \bold{ \green{b=8cm}}}}}}}$

☛Therefore , the Breadth of the rectangle is 8cm ..

✒Now ,

$\leadsto\sf\bold{Area\:of\:Square={(Side)}^{2}}$

$\dashrightarrow\sf{10cm\times{10cm}}$

$\dashrightarrow\sf{{100cm}^{2}}$

$\leadsto\sf\bold{Area\:of\:Rectangle=l\times{b}}$

$\dashrightarrow\sf{12cm\times{8cm}}$

$\dashrightarrow\sf{{96cm}^{2}}$

✒By how much : -

$\dashrightarrow\sf{{100cm}^{2}-{96cm}^{2}}$

$\leadsto\sf\bold{{4cm}^{2}}$

☛So , the square encloses more area ..

Answer 2

${ \huge{ \bold{\underline{ \underline{ \red{Solution:-}}}}}}$

${ \large{ \bold{\underline{ \underline{ \pink{Given:-}}}}}}$

Wire of a square shape = 10 cm

rebent of wire into a rectangle of length =12cm

${ \large{ \bold{\underline{ \underline{ \purple{To\: Find:-}}}}}}$

✰Find it's breadth

✰Which figure enclose more area and by how

${ \large{ \bold{\underline{ \underline{ \green{Formula:-}}}}}}$

$\large\mapsto{\tt{\blue{\:perimeter\: of\: the \: square\: = 4 × side}}}$

$\large\mapsto{\tt{4 × side}}$

$\large\mapsto{\tt{4 × 10 cm}}$

$\large\mapsto{\tt{40 cm}}$

We know that,

ꔷ Length of the rectangle = 12 cm

So,

● Perimeter of the rectangle = length of wire

${ \large{ \bold{\underline{ \underline{ \orange{Formula:-}}}}}}$

${\tt{\purple{\: perimeter\: of \:the \: rectangle\:2(l+b)}}}$

Now, putting the values,

$\large\mapsto{\tt{40 =2(12+b)}}$

$\large\mapsto{\tt{\frac{40}{2}(12+b)}}$

$\large\mapsto{\tt{b = 20-12}}$

$\mapsto\boxed{\tt{\pink{b = 8cm}}}$

Therefore,Breadth of the rectangle = 8 cm.

NoW,

$\leadsto{\bf{Area \:of\: the \:square \:=(side)^2}}$

$\large\leadsto{\tt{10×10}}$

$\large\leadsto{\tt{100cm^2}}$

$\large\leadsto{\tt{\: Area \: of \: the\: rectangle\: = l×b}}$

$\large\leadsto{\tt{12× 8}}$

$\large\leadsto{\tt{96cm^2}}$

By how much,

$\large\leadsto{\tt{100cm^2 -96cm^2}}$

$\large\leadsto{\tt{4cm^2}}$