CBSE Class 10-Mathematics: Chapter – 4 Quadratic Equations Part 15 (For CBSE, ICSE, IAS, NET, NRA 2022)

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Question 2:

Represent the following situations in the form of Quadratic Equations:

(i) The area of rectangular plot is . 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) The product of two consecutive numbers is . We need to find the integers.

(iii) Rohan՚s mother is years older than him. The product of their ages (in years) after years will be . We would like to find Rohan՚s present age.

(iv) A train travels a distance of at uniform speed. If, the speed had been less, then it would have taken hours more to cover the same distance. We need to find speed of the train.

Answer:

(i) We are given that area of a rectangular plot is .

Let breadth of rectangular plot be x meters

Length is one more than twice its breadth.

Therefore, length of rectangular plot is metres

Area of rectangle length breadth

This is a Quadratic Equation.

(ii)

Let two consecutive numbers be and .

It is given that

This is a Quadratic Equation.

(ii) Let present age of Rohan years

Let present age of Rohan՚s mother years

Age of Rohan after years years

Age of Rohan՚s mother after years years

According to given condition:

This is a Quadratic Equation.

(iv) Let speed of train be

Time taken by train to cover hours

If, speed had been less than time taken would be hours

According to given condition, if speed had been less then time taken is hours less.

Therefore,

Dividing equation by , we get

This is a Quadratic Equation.