Question

if length of a rectangle is increased by 5 cm and breadth decreased by 2 cm the area is unaltered. if length is decreased by 3 cm and breadth is increased by 2 cm even the area is unaltered. find length and breadth​

Answer 1

Answer:

x=15 cm ; y=8 cm

Step-by-step explanation:

let the actual length and breadth be x,y.

area of the rectangle is l×b=x×y=xycm^2-------i

length is increased by 5 cm=x+5cm

breadth is decreased by 2 cm=y-2cm

the area is unaltered

area of the rectangle is l×b=(x+5)(y-2)=

xy-2x+5y-10 cm^2=xy cm^2 ----------ii

length is decreased by 3 cm=x-3 cm

breadth is increased by 2cm=y+2 cm

the area is unaltered

area of the rectangle is l×b=(x-3)(y+2)=

xy+2x-3y-6 cm^2=xy cm^2 -------iii

xy-2x+5y-10 cm^2=xy cm^2 ----------ii

-2x+5y-10=0---------iv

xy+2x-3y-6 cm^2=xy cm^2 -------iii

2x-3y-6=0---------v

adding equation iv and v.

we get,

2y-16=0

2y=16

☆y=8 cm

substituting y value in equation iv

-2x+5y-10=0

-2x+40-10=0

-2x+30=0

-2x= -30

2x=30

☆x=15 cm

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Answer 2

Given : length of a rectangle is increased by 5 cm and breadth decreased by 2 cm the area is unaltered. if length is decreased by 3 cm and breadth is increased by 2 cm even the area is unaltered

To find :  length and breadth​ of rectangle

Solution:

Let say Length & breadth of rectangle =  L & B  cm

Area of Rectangle = LB

length of a rectangle is increased by 5 cm and breadth decreased by 2 cm

=> ( L + 5)(B - 2)  = LB

=> LB + 5B - 2L - 10 = LB

=> 5B - 2L = 10

length is decreased by 3 cm and breadth is increased by 2 cm  

=> ( L - 3)(B + 2) = LB

=> LB +2L - 3B - 6 = LB

=>  2L - 3B  = 6

Adding both

=> 5B - 3B  = 10 + 6

=> 2B = 16

=> B = 8

2L - 3B = 6

=> 2L - 3(8) = 6

=> 2L = 30

=> L = 15

Length = 15 cm   & Breadth = 8 cm

Verification :

Area 15 * 8  = 120

Area = (15 + 5)(8 - 2) = 20 * 6 = 120

Area = (15 - 3)(8 + 2) = 12 * 10 = 120

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