9. Length of a rectangle is 6cm more than its width . It’s length and breadth each is decreased by 3 cm , the area of new rectangle is decreased by 36 sq cm. Find the original length and breadth of the original rectangle ?
Answers
Answer:
original length = 10.5 cm and width = 4.5 cm. Step-by-step explanation: Let l be the length and w be the width of the rectangle. Now, the length and breadth is decreased by 3 cm the area of new rectangle decrease by 36 sq cm.
Answer:
cm
and the original Length of rectangle be = (x + 6) cm
Therefore, Original Area = Length × Breadth = (x + 6) × x = x2 + 6x
Now, New Length = (x + 6) - 3 = x + 6 - 3 = x + 3
New Breadth = x - 3
Therefore, New Area = Length × Breadth = (x + 3) × (x - 3) = (x)2 - (3)2 = x2 - 9
According to Question
Original Area - New Area = 36 sq cm.
(x2 + 6x) - (x2 - 9) = 36
x2 + 6x - x2 + 9 = 36
6x + 9 = 36
6x = 36 - 9
6x = 27
x = 276=92
Hence, Original Length of Rectangle = x + 6 = 92+6=9+122=212=10.5cm
Original Breadht of Rectangle = x = 92=4.5 cm
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