The perimeter of a rectangular garden is 420 cm. If its length is increased by 20% and breadth is decreased by 40%,we get the same perimeter. Then, the length and breadth of the new formed rectangular garden, respectively are
Answers
Answer:
- New length and breadth of garden would be 168 cm and 42 cm respectively.
Explanation:
Initially perimeter of rectangular garden is 420 cm
so, let length of garden be l and
breadth of garden be b
then,
→ 2 ( l + b ) = 420
→ l + b = 210
→ b = 210 - l ____equation (1)
Now, when length will be increased by 20% it will become
→ new length = l + (20 l / 100) = l + (l/5)
and breath on being decreased by 40% will become
→ new breadth = b - (40 b/100) = b - (2b/5)
then also we will get the same perimeter
therefore,
→ 2 [ ( l + (l/5) ) + ( b - (2b/5) ) ] = 420
→ 2 l + ( 2l/5 ) + 2 b - ( 4b/5 ) = 420
multiplying by 5 both sides
→ 10 l + 2 l + 10 b - 4 b = 2100
→ 12 l + 6 b = 2100
dividing by 6 both sides
→ 2 l + b = 350
Using equation (1)
→ 2 l + 210 - l = 350
→ l = 350 - 210
→ l = 140 cm
putting value of l in equation (1)
→ b = 210 - l
→ b = 210 - 140
→ b = 70 cm
So,
Length of new garden formed will be
→ new length = l + ( l/5 )
= 140 + ( 140/5 )
= 140 + 28
= 168 cm
and
→ new breadth = b - ( 2b/5 )
= 70 - ( 2(70)/5 )
= 70 - (140/5)
= 70 - 28
= 42 cm
Therefore,
- New length and breadth of garden would be 168 cm and 42 cm respectively.