Question

The area of the rectangle is 106cm². If it's length is 12cm. what is its perimeter.​

Answer 1

Step-by-step explanation:

${\large{\underline{\bold{\rm{Let's\ understand\ the\ concept\ 1^{st}:-}}}}}$

★ This question says that the Area of the Rectangle is 106cm². The length of the Rectangle is 12cm. Then firstly, we will find out the breadth of the Rectangle. After that, by applying the required values in the formula of Perimeter of Rectangle we will get the answer.

Let's do it !...

${\large{\underline{\bold{\rm{Given\ that:-}}}}}$

★ Area of Rectangle = 106cm².

★ Length of Rectangle = 12cm.

${\large{\underline{\bold{\rm{To\ find:-}}}}}$

★ In this question we have to find the Perimeter of Rectangle.

${\large{\underline{\bold{\rm{Using\ concepts:-}}}}}$

★ Formula of finding Area of Rectangle to find its breadth.

★ Formula of finding Perimeter of Rectangle.

${\large{\underline{\bold{\rm{Using\ formulas:-}}}}}$

★ Area of Rectangle = l × b.

★ Perimeter of Rectangle = 2(l + b).

${\large{\underline{\bold{\rm{Solution:-}}}}}$

★ Perimeter of Rectangle is approximately 41.66m.

${\large{\underline{\bold{\rm{Full\ solution:-}}}}}$

~ Now, finding breadth of the rectangle !...

↝ Area of Rectangle = l × b

↝ 106 = 12 × b

↝ b = 106/12

↝ b = 8.83.

${\sf{\pmb{\underline{\therefore Hence,\ breadth\ of\ rectangle\ =\ 8.83m.}}}}$

~ Now, finding perimeter of the rectangle !...

↝ Perimeter of Rectangle = 2(l + b)

↝ Perimeter of Rectangle = 2(12 + 8.83)

↝ Perimeter of Rectangle = 2(20.83)

↝ Perimeter of Rectangle = 2 × 20.83

↝ Perimeter of Rectangle ≈ 41.66m.

${\sf{\pmb{\underline{\therefore Hence,\ perimeter\ of\ rectangle\ is\ \approx\ 41.66m.}}}}$

Answer 2

Given: The area of the rectangle is 106cm² and the length is 12cm.

Need to find: The perimeter of the rectangle.

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⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀⠀⠀⠀⠀⠀⠀⠀

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${\underline{\bf{\dag}{\frak{\;As\;we\;know\;that\;:}}}}$

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$\star\;{\boxed{\pink{\sf{Area\;_{(rectangle)}=(Length×Breadth)}}}}$

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where,

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• Area of the rectangle is 106cm², length is 12cm and let the breadth be b.

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Therefore,

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$:\implies\sf{106=12×b}\\\\\\:\implies\sf{b=\dfrac{106}{12}}\\\\\\:\implies{\underline{\boxed{\purple{\frak{b=8.83\;cm}}}}{\;\bigstar}}$

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⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀⠀⠀⠀⠀⠀⠀⠀

★ As we know that, to calculate the perimeter of a rectangle formula is given by :

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$\star\;{\boxed{\pink{\sf{Perimeter\;_{(rectangle)}=2(l+b)}}}}$

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${\underline{\bf{\dag}{\frak{\;Substituting\;values\;:}}}}$

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$:\implies\sf{Perimeter\;_{(rectangle)}=2(12+8.83)\;cm}\\\\\\:\implies\sf{Perimeter\;_{(rectangle)}=(2×20.83)\;cm}\\\\\\:\implies{\underline{\boxed{\purple{\frak{Perimeter\;_{(rectangle)}=41.66\;cm}}}}}{\;\bigstar}$

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${\underline{\sf{Hence,\;the\;perimeter\;of\;the\;rectangle\;is\;{\bf{41.66\;cm}}}}.}$