the area of rectangle is decreased by 9 square meter if it's length decrases 5 meter and breadth increased by 3 meter. If it's length and breadth are increased by 3 meter and 2 meter each respectively it's area increase 67 square meter. find the length of the rectangle.
Answers
Answer:
The length of the rectangle is 17 m
Step-by-step explanation:
Given :
- The area of rectangle is decreased by 9 m² if it's length decreases by 5 m and breadth increased by 3 m.
- If it's length and breadth are increased by 3 m and 2 m each respectively it's area increases by 67 m².
To find :
the length of the rectangle
Solution :
Let the length of the rectangle be 'l' and breadth of the rectangle be 'b'
Area of the rectangle = l × b = lb
case - (i) :
length decreased by 5 m = (l - 5) m
breadth increased by 3 m = (b + 3) m
Area of the rectangle = (l - 5) (b + 3)
(lb - 9) = l(b + 3) - 5(b + 3)
lb - 9 = lb + 3l - 5b - 15
-9 = 3l - 5b - 15
3l - 5b = 15 - 9
3l - 5b = 6 ➙ [1]
case - (ii) :
length increased by 3 m = (l + 3) m
breadth increased by 2 m = (b + 2) m
Area of the rectangle = (l + 3) (b + 2)
(lb + 67) = l(b + 2) + 3(b + 2)
lb + 67 = lb + 2l + 3b + 6
67 = 2l + 3b + 6
2l + 3b = 67 - 6
2l + 3b = 61 ➙ [2]
Multiplying equation [1] by 3 and equation [2] by 5, we get
9l - 15b = 18 ➙ [3]
10l + 15b = 305 ➙ [4]
Adding equations [3] and [4],
9l - 15b + 10l + 15b = 18 + 305
19l = 323
l = 323/19
l = 17
Therefore, the length of the rectangle is 17 m