Question

The length and breadth of a rectangle are in a ratio 2:1. If length is increased by 2cm and breadth by 3cm then the ratio of the perimeter of the new rectangle to perimeter of the original rectangle is 4:3. Find the dimensions of original rectangle.

Answer 1

HERE IS UR ANSWER

Let the ratio be x as 1x:2x.

Perimeter of rectangle = 2(1x + 2x) = 6x  [ p = 2(l+b) ]

If length is increased by 2 and breadth is increased by 3 , then new perimeter = 2(x + 2 + 3 + 2x)

               = 6x + 10

(6x + 10)/6x = 4/3

3*(6x+10) = 24 X

18x + 30 = 24x

6x = 30

x = 5

Dimensions of Original Rectangle are 5 and 10 cm respectively..

HOPE IT HELPS UU..............

Answer 2

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

$\:\:$

$\green{\underline \bold{Given :}}$

$\:\:$

• 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

$\:\:$

$\red{\underline \bold{To \: Find:}}$

$\:\:$

• The dimensions of rectangle.

$\:\:$

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

$\:\:$

Let length be 'l'

Let breadth be 'b'

$\:\:$

$\purple{\underline \bold{According \: to \: the \ question :}}$

$\:\:$

$\purple\longrightarrow$ $\sf \dfrac { l } { b } = \dfrac { 1 } { 2 }$

$\:\:$

$\sf \longmapsto l = 2b$ -------(1)

$\:\:$

$\underline{\bold{\texttt{Length of new rectangle:}}}$

$\:\:$

$\purple\longrightarrow$ $\sf l + 2$

$\:\:$

$\underline{\bold{\texttt{Breadth of new rectangle:}}}$

$\:\:$

$\purple\longrightarrow$ $\sf b + 3$

$\:\:$

$\underline{\bold{\texttt{Perimeter of original rectangle:}}}$

$\:\:$

$\sf \longmapsto 2(l + b)$

$\:\:$

$\underline{\bold{\texttt{Perimeter of new rectangle:}}}$

$\:\:$

$\sf \longmapsto 2[(l + 2) + (b + 3)]$

$\:\:$

As per the question,

$\:\:$

$\sf \longmapsto \dfrac { 10 + 2l + 2b } { 2l + 2b } = \dfrac { 4 } { 3 }$

$\:\:$

$\sf \longmapsto 30 + 6l + 6b = 8l + 8b$

$\:\:$

$\sf \longmapsto 2l + 2b = 30$

$\:\:$

$\underline{\bold{\texttt{Dividing the above equation by 2}}}$

$\:\:$

$\sf \longmapsto l + b = 15$-------(2)

$\:\:$

$\underline{\bold{\texttt{Putting l = 2b in (2)}}}$

$\:\:$

$\sf \longmapsto 2b + b = 15$

$\:\:$

$\sf \longmapsto b = \dfrac { 15 } { 3 }$

$\:\:$

$\sf \longmapsto b = 5$

$\:\:$

$\underline{\bold{\texttt{Putting b = 5 in (1)}}}$

$\:\:$

$\sf \longmapsto l = 2(5)$

$\:\:$

$\sf \longmapsto l = 10$

$\:\:$

Hence length of rectangle will be 10 cm and breadth be 5 cm.

$\rule{200}5$