the area of a rectangle gets reduced by 20 square units , if its length is increased by 1 unit and breadth is reduced by 2 unit , if we reduce the length 3 unit and increase the breadth by 4 units then the area is increased by 12 square unit . Find the area of the rectangle .
Answers
Step-by-step explanation:
let the length be L
let the breath be B
case1: (L+1) (B-2) =LB-20
case2: (L-3) (B+4) =LB+12
from this we can get the value of L and B
The area would be 180 square units
Step-by-step explanation:
Let x be the length and y be the height of the rectangle,
∵Area of rectangle = length × width
So, the original area of the rectangle = xy,
Now, if length is increased by 1 unit and breadth is reduced by 2 unit,
New length = (x+1) unit, breadth = (y-2)
New area = (x+1)(y-2)
According to the question,
(x+1)(y-2)=xy-20
xy - 2x + y - 2 = xy - 20
y - 2x = -20 + 2
-2x + y = -18 .....(1)
Similarly, if we reduce the length 3 unit and increase the breadth by 4 units,
New area = (x-3)(y+4)
Again, according to the question,
(x-3)(y+4)=xy+12
xy + 4x - 3y - 12 = xy + 12
4x - 3y - 12 = 12
4x - 3y = 24 .....(2)
eq(2) + 2 × eq (1),
-3y + 2y = 24 - 36
-y = -12
⇒ y = 12
From eq (1),
-2x + 12 = -18
-2x = -18 - 12
-2x = -30
⇒ x = 15,
Hence, original area = 15 × 12 = 180 unit²
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