Question

A rectangular playground in 420 sq.m if the length is increased by7m and breadds is decrease by five meter the area remain is same. find the length and breadth of the playground.​

Answer 1

Answer:

21m and 20m

Step-by-step explanation:

Let the length and breadth of the playground be l and b respectively,

Therefore,

Area = l×b = 420 m²

=> b = 420/l —(1)

Now,

New length= l+7, New breadth = b-5

Area = (l+7)(b-5) =

Because area remains same,

(l+7)(b-5) = 420

=> lb -5l + 7b -35 = 420

=> 420 - 5l + 7b -35 = 420

=> 7b - 5l = 35

Using equation (1)

=> 7×420/l - 5l = 35

=> 7×84/l - l = 7

=> -l² + 7×84 = 7l

=> l²+7l - 588 = 0

=> l² - 21l + 28l - 588 = 0

=> l(l-21) + 28(l-21) = 0

=> (l-21)(l+28) = 0

=> l =21 m (Because, L can't be -28 which is negative)

b = 420/l = 20 m