If the length of a rectangle is decreased by 5 units and its breadth increased by 2 units then the area of the rectangle decreases by 80 square units. If its length is increased by 10 units and its breadth decreased by 5 units then the area of the rectangle increases by 50 square units. Find the original length and breadth of the rectangle.
Answers
Answer:
The length of the rectangle is 40 units and the breadth is 30 units.
Step-by-step explanation:
Let the length of the rectangle be l units and the breadth be b units.
Area of the rectangle = length × breadth
Area of the rectangle = lb sq. units
According to the first condition,
Length = (l - 5) units
Breadth = (b + 2) units
Area decreases by 80 sq. units.
Area = (lb - 80) sq. units
(l - 5)(b + 2) = lb - 80
l(b + 2) - 5(b + 2) = lb - 80
lb + 2l - 5b - 10 = lb - 80
2l - 5b - 10 = -80
2l - 5b = -80 + 10
2l - 5b = -70
2l = -70 + 5b
l = (-70 + 5b)/2
l = -35 + 2.5b --(1)
According to the second condition,
length = (l + 10) units
Breadth = (b - 5) units
Area of the rectangle increased by 50 sq. units
Area = (lb + 50) sq. units
(l + 10)(b - 5) = lb + 50
l(b - 5) + 10(b - 5) = lb + 50
lb - 5l + 10b - 50 = lb + 50
10b - 5l = 50 + 50
10b - 5l = 100
2b - l = 20
2b - (-35 + 2.5b) = 20
2b + 35 - 2.5b = 20
-0.5b = -35 + 20
-0.5b = -15
0.5b = 15
b = 15/0.5
b = 30 units
Length, l = -35 + 2.5b
l = -35 + 2.5(30)
l = -35 + 75
l = 40 units
Therefore, the length of the rectangle is 40 units and the breadth is 30 units.
Answer:
Step-by-step explanation:
Let the length of the rectangle be l units and the breadth be b units.
Area of the rectangle = length × breadth
Area of the rectangle = lb sq. units
As per the question
Length = (l - 5) units
Breadth = (b + 2) units
Area decreases by 80 sq. units.
Area = (lb - 80) sq. units
(l - 5)(b + 2) = lb - 80
l(b + 2) - 5(b + 2) = lb - 80
lb + 2l - 5b - 10 = lb - 80
2l - 5b - 10 = -80
2l - 5b = -80 + 10
2l - 5b = -70
2l = -70 + 5b
l = (-70 + 5b)/2
l = -35 + 2.5b --(1)
According to the second condition,
length = (l + 10) units
Breadth = (b - 5) units
Area of the rectangle increased by 50 sq. units
Area = (lb + 50) sq. units
(l + 10)(b - 5) = lb + 50
l(b - 5) + 10(b - 5) = lb + 50
lb - 5l + 10b - 50 = lb + 50
10b - 5l = 50 + 50
10b - 5l = 100
2b - l = 20
2b - (-35 + 2.5b) = 20
2b + 35 - 2.5b = 20
-0.5b = -35 + 20
-0.5b = -15
0.5b = 15
b = 15/0.5
⇒b = 30 units
Length, l = -35 + 2.5b
= -35 + 2.5(30)
= -35 + 75
= 40 unit