Question

The area of a rectangle is same as that of a square of side 16 m. If the length of the rectangle is 32 m, find its perimeter.​

Answer 1

Step-by-step explanation:

As we know that,

Area of square =a2

Here a is the length of side of square.

Therefore,

Area of given square =162=256cm2

Length of rectangle =32cm

Area of rectangle = Area of square (Given)

Therefore,

Area of rectangle =l×b

b×32=256

⇒b=32256=8cm

Hence the breadth of rectangle is 8cm.

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Answer 2

$\large{\sf{ \blue{Question\!\!: }}}$

The area of a rectangle is same as that of a square of side 16 m. If the length of the rectangle is 32 m, Find its perimeter.

$\large{\sf{ \blue{To\:find\!\!: }}}$

• Perimeter of rectangle

$\large{\sf{ \blue{Given\!\!: }}}$

• Area of rectangle=Area of square

• Side of square= 16m

• The length rectangle= 32m

$\large{\sf{ \blue{Formula\: Used\!\!: }}}$

• $\sf{Area \: of \:square = {side}^{2}}$

• $\sf{Width=\dfrac{Area}{Length} }$

• $\sf{Perimeter \: of \: rectangle \: = \: 2 \: ( \: Length \: + \: Width \: ) \: }$

$\large{\sf{ \blue{Answer\!\!: }}}$

First let's find Area of square:

We know:

$\green{ \underline{ \boxed{ \sf{Area \: of \:square = {side}^{2} }}}}$

By using this formula we can find value of Area of square.

$: \implies \sf{Area \: of \:square = {16}^{2} }$

$: \implies \sf{Area \: of \:square = 16 \: m\times 16 \: m}$

$: \implies \star \boxed{ \sf{Area \: of \:square = 256 {m}^{2}} } \star$

According to question:

Area of square = Area of rectangle

∴ Area of rectangle=256m²

Now we can find value of width by using this formula:

$\green{ \underline{ \boxed{ \sf{Width=\dfrac{Area}{Length} }}}}$

$: \implies \sf{Width=\dfrac{256}{32} }$

$: \implies \sf{Width=\dfrac{ { \cancel{256}}^{ \: 8} }{ { \cancel{32}}^{ \: 1} } }$

$: \implies \star \boxed{ \sf{Width=8 \: m}} \star$

Now finally let's find what's asked i.e. perimeter of rectangle.

We know:

$\green{ \underline{ \boxed{ \sf{Perimeter \: of \: rectangle \: = \: 2 \: ( \: Length \: + \: Width \: ) \: }}}}$

Using this formula we can find value of perimeter.

$: \implies\sf{}Perimeter \: of \: rectangle=2(32 +8)$

$: \implies\sf{}Perimeter \: of \: rectangle=2(40)$

$: \implies \star \boxed{\sf{}Perimeter \: of \: rectangle=80 \: m} \star$