The length and the breadth of a rectangle are in the ratio 2:1. If the length is increased by 2 cm and breadth by 3 cm then the ratio of the perimeter of the new rectangle to the perimeter of the original rectangle is 4/3. Find the dimensions of the original rectangle.
Answers
Answer:
Ratio of length and breadth of a rectangle is 2:1
When 2 is added to length and 3 is added to breadth then ratio of perimeter of new rectangle to original rectangle is 4:3
\:\:
\red{\underline \bold{To \: Find:}}
ToFind:
\:\:
The dimensions of rectangle.
\:\:
\large{\orange{\underline{\tt{Solution :-}}}}
Solution:−
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Let length be 'l'
Let breadth be 'b'
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\purple{\underline \bold{According \: to \: the \ question :}}
Accordingtothe question:
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\purple\longrightarrow⟶ \sf \dfrac { l } { b } = \dfrac { 1 } { 2 }
b
l
=
2
1
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\sf \longmapsto l = 2b⟼l=2b -------(1)
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\underline{\bold{\texttt{Length of new rectangle:}}}
Length of new rectangle:
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\purple\longrightarrow⟶ \sf l + 2l+2
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\underline{\bold{\texttt{Breadth of new rectangle:}}}
Breadth of new rectangle:
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\purple\longrightarrow⟶ \sf b + 3b+3
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\underline{\bold{\texttt{Perimeter of original rectangle:}}}
Perimeter of original rectangle:
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\sf \longmapsto 2(l + b)⟼2(l+b)
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\underline{\bold{\texttt{Perimeter of new rectangle:}}}
Perimeter of new rectangle:
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\sf \longmapsto 2[(l + 2) + (b + 3)]⟼2[(l+2)+(b+3)]
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As per the question,
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\sf \longmapsto \dfrac { 10 + 2l + 2b } { 2l + 2b } = \dfrac { 4 } { 3 }⟼
2l+2b
10+2l+2b
=
3
4
\:\:
\sf \longmapsto 30 + 6l + 6b = 8l + 8b⟼30+6l+6b=8l+8b
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\sf \longmapsto 2l + 2b = 30⟼2l+2b=30
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\underline{\bold{\texttt{Dividing the above equation by 2}}}
Dividing the above equation by 2
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\sf \longmapsto l + b = 15⟼l+b=15 -------(2)
\:\:
\underline{\bold{\texttt{Putting l = 2b in (2)}}}
Putting l = 2b in (2)
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\sf \longmapsto 2b + b = 15⟼2b+b=15
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\sf \longmapsto b = \dfrac { 15 } { 3 }⟼b=
3
15
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\sf \longmapsto b = 5⟼b=5
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\underline{\bold{\texttt{Putting b = 5 in (1)}}}
Putting b = 5 in (1)
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\sf \longmapsto l = 2(5)⟼l=2(5)
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\sf \longmapsto l = 10⟼l=10
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Hence length of rectangle will be 10 cm and breadth be 5 cm.
\rule{200}5
Answer:
let length and breadth be 2x,1x
now,
new length= 2x +2
new breadth=1x+3
let ratio of perimeter of new and original rectangle be 4x,3x
so,
p= 2(l+b)
3x=2(2x+1x)
3x=6x
now,
p of new rectangle=4x
4x=2(2x+2+1x+3)
4x=4x+4+2x+6
4x=6x+10
-2x=10
x=-5