Question

if the length and breath of a rectangle are double by what percentage is the area increased​

Answer 1

$\huge{\blue{\bold{\underline{\underline{Answer :}}}}}$

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$\large\underline{\green{\bf Given :-}}$

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• Length and breath of a rectangle are doubled

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$\large\underline{\red{\bf To \: Find :-}}$

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• What percentage is the area increased

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$\large\underline{\orange{\bf Solution :-}}$

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• Let the original length be "l"

• Let the original breadth be "b"

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We know that,.

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$\underline{\bold{\texttt{Area of rectangle :}}}$

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➠ Length × Breadth

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$\underline{\bold{\texttt{Original Area :}}}$

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➜ Length × Breadth

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➜ l × b

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➨ lb ⚊⚊⚊⚊ ⓵

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$\underline{\bold{\texttt{Length when doubled :}}}$

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➠ 2(l)

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$\underline{\bold{\texttt{Breadth when doubled :}}}$

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➠ 2(b)

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$\underline{\bold{\texttt{Area of rectangle with new dimensions :}}}$

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➜ Length × Breadth

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➜ 2(l) × 2(b)

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➨ 4(lb) ⚊⚊⚊⚊ ⓶

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$\underline{\bold{\texttt{Increased area :}}}$

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⟮ Equation ⓶ - ⓵ ⟯

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➜ 4(lb) - (lb)

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➨ 3(lb)

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$\underline{\bold{\texttt{Percentage of area increased :}}}$

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➠ $\sf \dfrac { Increased \: Area } { Original \: Area } × 100$

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➜ $\sf \dfrac { 3(lb) } { lb } × 100$

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➜ 3 × 100

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➨ 300 %

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• Hence there will be 300% increase in area when its length and breadth are doubled

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Answer 2

$\huge\underline{\bf \orange{AnSweR :}}$

Let the original length be "l"

Let the original breadth be "b"

We know that,

Area of rectangle :

=> Length × Breadth

Original Area :

➜ Length × Breadth

➜ l × b

➨ lb ⚊⚊⚊⚊ ⓵

Length when doubled

=> 2(l)

Breadth when doubled :

=> 2(b)

Area of rectangle with new dimensions :

➜ Length × Breadth

➜ 2(l) × 2(b)

➨ 4(lb) ⚊⚊⚊⚊ ⓶

Increased area :

⟮ Equation ⓶ - ⓵ ⟯

➜ 4(lb) - (lb)

➨ 3(lb)

Percentage of area increased

=> OriginalArea IncreasedArea ×100

➜ lb3(lb) ×100

➜ 3 × 100

➨ 300 %

Hence there will be 300% increase in area when its length and breadth are doubled.