Question

Question Number: 24
The length and breadth of a rectangular plot are is the ratio 3:2. When the length and breadth of the plot are increased by 3 meters and 2 meters respectively,
the area increases by 54 m? What is the original length and breadth of the plot?​

Answer 1

Explanation:

Let l be the length and b be the breadth of the plot.

lb=32

2l=3b -- ( 1 )

Original area = l∗b

conditon of "When length and breadth are increased by 3 and 2 meters ",

(l+3)(b+2)=lb+54

lb+2l+3b+6=lb+54

2l+3b=48

Using (1 ) above,

3b+3b=48

b=486=8m

l=3∗82=12m

Answer 2

actual length=12cm and breadth=8cn

Explanation:

actual ratio=3:2=3x:2x actual

area=3x*2x=6x^2

new length=3x+3 new width=2x+2

area increased= 54m,new area=6x^2+54

area= l*b=(3x+3)(2x+2)=6x^2+12x+6

so,new area-6x^2+54=6x^2+12x +6

so,54=12x +6

12x=54-6=48

x=48/4=12

actual length=3x=12 cm

actual breadth=2x= 8 cm