Question

the perimeter of a rectangle is 120 m . if it's length is decreased by 10% and its breadth is increased by 20% the perimeter does not change . find the dimensions of rectangle​

Answer 1

❥${\purple{\underline{\underline{\large{\mathtt{ANSWER:-}}}}}}$

Length of the rectangle is 40 m. and breadth of rectangle is 20 m.

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❥${\purple{\underline{\underline{\large{\mathtt{EXPLANATION:-}}}}}}$

• Given:-

• Perimeter of rectangle= 120 m.
• If its length is decreased by 10% and its breadth is increased by 20% ,the perimeter does not change.

•To find:-

• Dimensions of rectangle.

• Solution:-

Let the length of rectangle be x m and the breadth of rectangle be y m.

Perimeter of rectangle= 120 m.

We know,

$\large{\boxed{\sf{\red{Perimeter\:of\: rectangle=2(length+breadth)}}}}$

So,

Perimeter of rectangle=2(l+b)

=2(x+y) m.

★ According to the question,

${\sf{2(x+y)= 120}}$

${\sf{\implies{x+y=60}}}$

${\sf{\green{\implies{x=60-y..........(i)}}}}$

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ᴥ Length is decreased by 10% .

${\sf{Length=x - x×\frac{10}{100}\:m}}$

${\sf{→Length=\frac{9x}{10}\:m}}$

ᴥ Breadth is increased by 20%.

${\sf{Breadth=y + y×\frac{20}</p><p>{100}\:m}}$

${\sf{→Breadth=\frac{6y}{5}\:m}}$

Now, the perimeter of rectangle,

${\sf{2(\frac{9x}{10}+\frac{6y}{5})\:m}}$

${\sf{=2(\frac{9x+12y}{10})\:m}}$

★ According to the question,

${\sf{2(\frac{9x+12y}{10})=120}}$

${\sf{→\frac{9x+12y}{10}=60}}$

${\sf{→9x+12y=600}}$

† Putting the value of x=60-y †

${\sf{→9(60-y)+12y=600}}$

${\sf{→540-9y+12y=600}}$

${\sf{→-9y+12y=600-540}}$

${\sf{→3y=60}}$

${\sf{→y=20}}$

Breadth = 20 m.

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✞ Putting the value of y= 20 in (i) no. equation✞

x= 60 - y

→ x = 60-20

→ x = 40

Length = 40 m.

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❥${\underline{\underline{\large{\mathtt{VERIFICATION:-}}}}}$

Length = 40 m

Breadth = 20 m.

Perimeter = 120 m.

So,

2(40+20) = 120

→ 120 = 120 (Verified)

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Answer 2

$\huge{ \underline{ \underline{ \green{ \sf{ Detailed \: Answer :}}}}}$

Given :

Perimeter of a rectangle is 120m.

To find :

Dimensions of rectangle

${\red{\huge{\underline{\mathbb{Answer:-}}}}}$

let the length of rectangle be l and breadth be b .

we know that :

${\purple{\boxed{\large{\bold{Perimeter \: of \: a \: rectangle = 2( l + b ) }}}}}$

P = 2(l + b)

⇒120= 2(l+b)

⇒l+ b = 60 .....(1)

According to the Question :

length is decreased by 10%

⇒length = l -10% of l

⇒length = l -$\frac{l}{10}$

⇒length= 0.9 l

and breadth is increased by 20%

⇒breadth = b+ 20% of b

⇒breadth = b + $\frac{b}{20}$

⇒breadth = 1.2 b

Now new perimeter of rectangle

P' = 2(l+b)

P' = 2(0.9 l + 1.2 b)

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Given :

perimeter of rectangle doesn't change .ie

${\red{\boxed{\large{\bold{Inital \:Perimeter = New \: perimeter }}}}}$

P = P'

120 = 2(0.9 l +1.2 b)

60 = 0.9l +1.2 b .....(2)

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on comparing equation (1) and (2)

l + b = 0.9 l + 1.2 b

⇒l - 0.9 l = 1.2 b - b

⇒0.1 l = 0.2 b

⇒ l = 2b .....(3)

put l = 2b in equation (1)

⇒2b + b = 60

⇒3b = 60

⇒b = 20

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∴Dimensions of rectangle :

Length ,l = 2b = 2× 20= 40 m

breadth ,b = 20 m