Question

The perimeter of a rectangle i 20 cm. If length exceeds breadth by 4 cm, find the area of the rectangle
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Answer 1

Given: Perimeter of a rectangle is 20 cm & the length exceeds the breadth by 4 cm.

Need to find: Area of the rectangle?

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❍ Let the breadth be x and according to the question, length be (x + 4) respectively.

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As we know that,

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

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Therefore,

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$:\implies\sf{2(x+4+x)=20}\\\\\\:\implies\sf{2x+4=\dfrac{20}{2}}\\\\\\:\implies\sf{2x+4=10}\\\\\\:\implies\sf{2x=10-4}\\\\\\:\implies\sf{2x=6}\\\\\\:\implies\sf{x=\dfrac{6}{2}}\\\\\\:\implies\underline{\boxed{\frak{\pmb{x=3}}}}\;\bigstar$

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Hence,

• Length of the rectangle = (x + 4) = 7 cm
• Breadth of the rectangle = x = 3 cm

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We know that, to calculate the area of a rectangle formula is given by:

• Area = Length × Breadth

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$\twoheadrightarrow\sf{Area=7\times 3}\\\\\\\twoheadrightarrow\sf{Area=21\;cm^2}$

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$\therefore\;\underline{\sf{Hence,\;the\;area\;of\;the\; rectangle\;is\;\bf{21\;cm^2}}.}$⠀⠀⠀