Question

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.
(i) The product of two consecutive positive integers is 306. We need to find the
integers.
(iii) Vinay's mother is 26 years older than him. The product of their ages (in years)
years
from now will be 360. We would like to find Vinay's present age.
(iv) 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 3 hours more to cover the same distance.
We need to find the speed of the train.
3​

Answer 1

I hope it is useful to you

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Answer 2

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(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

⇒ 2x^2 + x = 528

⇒ 2x^2 + 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 more to cover the same distance.

Therefore, time taken to travel 480 km = (480/x) + 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

⇒ 3x^2 – 24x – 3840 = 0

⇒ x^2 – 8x – 1280 = 0

Hence, x^2 – 8x – 1280 = 0 is the required representation of the problem mathematically

Hope it's Helpful.....:)