Represent the following situations in the form of quadratic equations:
(i) The area of a rectangular plot is 528 m2. The length of the plot (in metres) is one more than twice its breadth. We need to find the length and breadth of the plot.
(ii) A train travels a distance of 480 km at a uniform speed. If the speed had been 8 km/h less, then it would have taken.
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Answers
Answer:
Solution:
(i) Let us consider,
The breadth of the rectangular plot is x m
Thus, the length of the plot = (2x + 1) m.
As we know,
Area of rectangle = length × breadth = 528 m2
Putting the value of length and breadth of the plot in the formula, we get,
(2x + 1) × x = 528
⇒ 2x2 + x =528
⇒ 2x2 + x – 528 = 0
Hence, 2x2 + x – 528 = 0, is the required equation which represents the given situation.
(ii) Let us consider,
speed of train = x km/h
And
Time taken to travel 480 km = 480 (x) km/h
As per second situation, the speed of train = (x – 8) km/h
As given, the train will take 3 hours to cover the same distance.
Therefore, time taken to travel 480 km = 480x + 3 km/h
As we know,
Speed × Time = Distance
Therefore, time taken to travel 480 km = 480x + 3 km/h
As we know,
Speed × Time = Distance
Therefore,
(x – 8)(480/x + 3) = 480
⇒ 480 + 3x – 3840/x – 24 = 480
⇒ 3x – 3840/x = 24
⇒ 3x2 – 8x – 1280 = 0
Hence, 3x2 – 8x – 1280 = 0 is the required representation of the problem mathematically.
hope it helps u.......
Represent the following situations in the form of quadratic equations:
(i) The area of a rectangular plot is 528 m2. The length of the plot (in metres) is one more than twice its breadth. We need to find the length and breadth of the plot.
answer in pic (1)
A train travels a distance of 480 km at a uniform speed. If the speed had been 8 km/h less, then it would have taken.
answer in pic
