the area of a rectangle gets reduced by 9 sq units. If its lenght us reduced by 5 units and breadth is increased by 3 units. The area is increased by 67 sq units, if lenght is increased by 3 units and breadth is increased by 2 units. Find perimeter of a rectangle?
Answers
Answer:
L = 17 units b = 9units p=2(l+b) = 52 units
Step-by-step explanation:
Given :-
The area of a rectangle gets reduced by 9 sq units. If its lenght is reduced by 5 units and breadth is increased by 3 units. The area is increased by 67 sq units, if the lenght is increased by 3 units and breadth is increased by 2 units.
To find :-
Find perimeter of a rectangle?
Solution :-
Let the length of a rectangle be l units
Let the breadth of the rectangle be b units
Area of the rectangle = lb sq.units
Condition -1:-
If the length is reduced by 5 units then the new length = (l-5) units
If the breadth is increased by 3 units then the new breadth = (b+3) units
Then,
The area = (l-5)(b+3) sq.units
The area of a rectangle gets reduced by 9 sq units. If its lenght is reduced by 5 units and breadth is increased by 3 units.
=> (l-5)(b+3) = lb-9
=> l(b+3)-5(b+3) = lb-9
=> lb+3l-5b-15 = lb-9
=> 3l-5b-15 = -9
=> 3l-5b = -9+15
=> 3l-5b = 6 ------------(1)
=> 6l -10b = 12 ----------(2)
Condition -2:-
If the length is increased by 3 units then the new length = (l+3) units
If the breadth is increased by 2 units then the new breadth = (b+2) units
Then,
The area = (l+3)(b+2) sq.units
The area is increased by 67 sq units, if the lenght is increased by 3 units and breadth is increased by 2 units.
=> (l+3)(b+2) = lb+67
=> l(b+2)+3(b+2) = lb+67
=> lb+2l+3b+6 = lb+67
=> 2l+3b+6= 67
=> 2l+3b = 67-6
=> 2l+3b = 61
=> 6l+9b = 183------------(3)
On Subtracting (1) from (3) then
6l+9b = 183
6l- 10b = 12
(-)
_________
19b = 171
_________
=> 19b = 171
=> b = 171/19
=> b = 9 units
The breadth = 9 units
On Substituting the value of b in (1) then
3l-5b = 6
=> 3l -5(9) = 6
=> 3l - 45 = 6
=> 3l = 6+45
=> 3l =51
=> l = 51/3
=> l = 17
The length = 17 units
We know that
The perimeter of a rectangle = 2(l+b) units
=> P = 2(17+9)
=> P = 2(26)
=> P = 52 units
Answer:-
The perimeter of the given rectangle is 52 units
Check :-
l = 17 units and b = 9 units
Area = 17×9= 153 sq units
The area of a rectangle gets reduced by 9 sq units. If its lenght is reduced by 5 units and breadth is increased by 3 units.
=> (17-5)×(9+3)
=> 12×12
=>144
Decreasing in the area = 153-144 = 9 sq.units
and
The area is increased by 67 sq units, if the lenght is increased by 3 units and breadth is increased by 2 units.
=> (17+3)×(9+2)
=> 20×11
=> 220 sq.unis
Increasing in the area = 220-153 = 67 sq.units
Verified the given relations in the given problem.
Used formulae:-
→Area of the rectangle = lb sq.units
→The perimeter of a rectangle = 2(l+b) units
→ l = length
→ b = breadth