The perimeter of a rectangle is 240m. If its length is decreased by 10% and breadth is increased by 20% we get the same perimeter. Find the length and the breadth of the both the rectangles.
Answers
Let the length be x
100 - 10 = 90%
90% = 0.9
⇒ length after 10% reduced = 0.9x
.
Let the breadth be y
100 + 20 = 120%
120% = 0.12
⇒ breadth after 20% increased = 1.2y
.
Form equations:
2 (x + y) = 240 ------------------- [ 1 ]
2(0.9x + 1.2y) = 240 ------------- [ 2 ]
.
From [ 1 ]:
2 (x + y) = 240
x + y = 120
x = 120 - y ------------- [ 3 ]
.
From [ 2 ] :
2(0.9x + 1.2y) = 240
0.9x + 1.2y = 120 ------------- [ 4 ]
.
Substitute [ 3 ] into [ 4 ] :
0.9 (120 - y) + 1.2y = 120
108 - 0.9y + 1.2 y = 120
0.3y = 12
y = 40
.
Substitute y = 40 into [ 3 ]:
x = 120 - 40
x = 80
.
Find the length and Breadth:
Length = x = 80 m
Breadth = y = 40 m
.
Find the length and breadth after the changes:
Length = 0.9(x) = 0.9(80) = 72 m
Breadth = 1.2 (y) = 1.2 (40) = 48 m
,
Answer:
Before: Length = 80 m and Breadth = 40 m.
After: Length = 72 m and Breadth = 48 m
Answer:
Step-by-step explanation:
Solution:-
Let the length and breadth of the rectangle be x m and y m.
According to the Question,
⇒ x + y = 120 .... (i)
Length = x(100 - 10)/100
= 9x/10
Breadth = y(100 +20)/100
= 12y/10
Perimeter of rectangle = 240 m
2(L + B) = 240
⇒ 2(9x /10 + 12y /10) = 240
⇒ 9x + 12y = 1200
⇒ 3x + 4y = 400 .... (ii)
Solving Eq (i) and (ii), we get
⇒ y = 40
Putting y's value in Eq (i), we get
⇒ x + y = 120
⇒ x + 40 = 120
⇒ x = 120 - 40
⇒ x = 80
Length = x = 80 m
Breadth = y = 40 m
Hence, the length and the breadth of the rectangle are 40 m and 80 m.