Question

if the length of a rectangle is tripled and its breath is doubled , what will happen to the area of this rectangle ? find the ratio of the area of resultant ractangle to the area of the orginal rectangle.


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# Moderator challenge​

Answer 1

Given:-

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The length of a rectangle is tripled and its breadth is doubled

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To Find:-

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what will happen to the area of this rectangle

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the ratio of the area of resultant ractangle to the area of the original rectangle

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STEP BY STEP EXPLANATION:-

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$\sf \longrightarrow let \: the \: length \: and \: breadth \: of \: a \: rectangle \: are \: x \: only \\ \\ \sf \longrightarrow area = x \times y = xy \\ \\ \sf \longrightarrow if \: length \: is \: tripled \: than \: the \: new \: = 3x \\ \\ \sf \longrightarrow if \: the \: breadth \: is \: doubled \: than \: the \: new \: breadth = 2y \\ \\ \sf \longrightarrow area = 3x \times 2y = 6xy \\ \\ \sf \longrightarrow then \: the \: area \: become \: 6 \: times \: of \: the \: previous \: area \: ratio \\ \\ \sf \longrightarrow \frac{6xy}{xy} = 6: 1 \\ \\ \sf \therefore so \: the \: ratio \: of \: the \: area \: resultant \: rectangle \: to \: the \: area \: of \: the \: original \: rectangle = 6: 1$

Answer 2

Step-by-step explanation:

ANSWER:-

• Let the length of the wire be l.
• Let the breadth of wire be b.

So. the original Area is

$lb = area$

As we know that:-

• Area of a triangle = length× breadth.

So,

• Now length is 3l
• Now length is 2b.

Area = l×b

$= 3l \times 2b$

$= 6lb$

Now , putting in terms of Ratio,

Area of 1st : Area of 2nd case,

$\frac{lb}{6lb}$

$\frac{ \cancel{lb}}{6 \cancel{lb}}$

So, area stands in Ratio of

1:6 is the answer.

Things to Note:-

• Perimeter = 2×(Length+Breadth)
• Area = length× breadth
• The length and breadth of a rectangle can never be same.
• If it is, so it will be a square.
• Hence we will never take same character for length and breadth.