Question

the area of rectangle get reduced by 8m2 when its length is reduced by 5m and breadth increase by 3m if we increase the length by 3m and breadth by 2m the area is increased bt 74m2.find the length breadth of rectangle by linear equation​

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Answer 1

Answer:

Step-by-step explanation:

given

let area be a

length be l

breadth be b

a-8=(l-5)(b+3)

a=(lb+3l-5b-15+8)

=lb+3l-5b-7--(1)

a+74=(l+3)(b+2)

a=lb+2l+3b+6-74

=lb+2l+3b-68---(2)

(1)=(2)

lb+3l-5b-7=lb+2l+3b-68

l-8b+61=0

l+61=8b--(3)

b=l+61/8

and length=8b-61

As there are two equations and three unknowns we cant solve the equations

Answer 2

Answer:

HOPE THIS HELP YOU

Step-by-step explanation:

Let the length and the breadth of the rectangle be x m and y m, respectively.

∴ Area of the rectangle = (xy) sq.m  

Case 1:  When the length is reduced by 5m and the breadth is increased by 3 m:

New length = (x – 5) m  

New breadth = (y + 3) m  

∴ New area = (x – 5) (y + 3) sq.m  

∴ xy – (x – 5) (y + 3) = 8  

⇒ xy – [xy – 5y + 3x – 15] = 8  

⇒ xy – xy + 5y – 3x + 15 = 8  

⇒ 3x – 5y = 7 ………(i)  

Case 2:  When the length is increased by 3 m and the breadth is increased by 2 m:  

New length = (x + 3) m  

New breadth = (y + 2) m  

∴ New area = (x + 3) (y + 2) sq.m  

⇒ (x + 3) (y + 2) – xy = 74  

⇒ [xy + 3y + 2x + 6] – xy = 74  

⇒ 2x + 3y = 68 ………(ii)

On multiplying (i) by 3 and (ii) by 5, we get:  

9x – 15y = 21 ……….(iii)  

10x + 15y = 340 ………(iv)  

On adding (iii) and (iv), we get:  

19x = 361  ⇒ x = 19  

On substituting x = 19 in (iii), we get:  

9 × 19 – 15y = 21  

⇒171 – 15y = 21  

⇒15y = (171 – 21) = 150  

⇒y = 10  

Hence, the length is 19m and the breadth is 10m.