Question

If the length of a rectangle is increased by 5 metres and the breadth decreased by 3 metres the area would decrease by 5 metre if the length is increased by 3 metres and breadth increased by 2 metre the area would increased by 50 metres what are the length and breadth

Answer 1

Answer:

length = 10

breadth = 8

Step-by-step explanation:

let length be l and breadth be b

area will be = l × b

length is increased by 5m

l + 5

breadth is decreased by 3m

b - 3

area will be = (l + 5)(b - 3) = lb - 5

$lb - 3l + 5b - 15 = lb - 5 \\ - 3l + 5b = 10 \: \: \: \: equ \: (1)$

length is increased by 3m

breadth is increased by 2m

area will increase by 50m

$(l + 3)(b + 2) = lb + 50 \\ lb + 2l + 3b + 6 = lb + 50 \\ 2l + 3b = 44 \: \: \: \: equ \: (2)$

multiply equ (1) with 2 and equ (2) with 3

-6l + 10b = 20

6l + 9b = 132

adding the equation we get

19b = 152

b = 152/19 = 8

substitute b in equ (2)

2l + 3(8) = 44

2l + 24 = 44

2l = 44 - 24 = 20

l = 20/2 = 10

therefore

length = 10

breadth = 8