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

Answer:

L = 10cm  B = 5cm

Step-by-step explanation:

let the length of rectangle be x

And the breadth of the rectangle be y

x : y = 2 : 1

new length = x + 2

new breadth= y + 3

ratio of new perimeter to old perimeter = 4 : 3

2 ( x + 2 + y + 3 ) : 2 ( x + y ) = 4 : 3

( x + y +5 ) : ( x + y ) = 4 : 3

$\large{\frac{x+y+5}{x+y}=\frac{4}{3}}\\\\\large{\frac{x+y}{x+y}+\frac{5}{x+y}=1+\frac{1}{3}}\\\\\large{1+\frac{5}{x+y}=1+\frac{1}{3}}\\\\\large{\frac{5}{x+y}=\frac{1}{3}}\\\\\large{x+y=15.......1}\\\\\large{Given}\\\\\large{x:y=2:1}\\\\\large{\frac{x}{y}=2}\\\\\large{x=2y.........2}\\\\\large{Sub\;\;2\;\;in\;\;1}\\\\\large{2y+y=15}\\\\\large{3y=15}\\\\\large{y=5}\\\\\large{x=10}$

Length = 10cm

Breadth = 5cm

Hope it Helps

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.

$\rule{200}5$