Question

If the · Length and breadth of a Tectangle
are a increased 3m and 2m respectively,
the area would increase by 52 sq.m.
If the length and breadth are decreased
by 2m and 3m respectively, the area
would decreased by 43 sq.m. Find the
Length and breadth of the rectangle:​

Answer 1

Answer:

length= 11m breadth= 8m

Step-by-step explanation:

let the length and breadth of rectangle are x&y

A.T.Q.

Case_1 :

(x+3)(y+2) = xy+52

xy+2x+3y+6 = xy+52

on cancelling xy from both sides and sending (+6) to RHS

2x+3y = 46_eq`1

Case_2 :

(x-2)(y-3) = xy-43

xy-3x-2y+6 = xy-43

on cancelling xy from both sides and sending (+6) to RHS

-3x-2y = -49_eq`2

on eq`1×3 & eq`2×2 and add them

so,

6x+9y = 138

-6x-4y = -98

equals to: 5y = 40

then, y = 8 (breadth)

putting y = 8 in eq`1

2x+3(8) = 46

2x+24 = 46

2x = 22

x = 11 (length)

so, length & breadth of rectangle are 11 & 8 respectively

Answer 2

Step-by-step explanation:

Let l be length of rectangle

b be the breadth of rectangle

(l+3)(b+2)=52

lb+2l+3b+6=lb+52

2l+3b=46. (1)

(l-2)(b-3)=lb-43

lb-3l-2b+6=lb-43

-(3l+2b)= -37

3l+2b=37. (2)

by elimination method

multiply (1)×3 and (2)×2

by solving we get answer

may be answer will be

l=19/5

b=64/5