Represent the following situations in the form of quadratic equations : (i) The area of a rectangular plot is 528 `m^2`. 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 positive integers is 306. We need to find the integers.
(iii) Rohan’s mother is 26 years older than him. The product of their ages (in years) 3 years from now will be 360. We would like to find Rohan’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.
Text Solution
AI Generated Solution
To represent the given situations in the form of quadratic equations, we will break down each part step by step.
### (i) Area of a rectangular plot
1. **Define Variables**: Let the breadth of the rectangle be \( x \) meters. Then, the length of the rectangle is \( 2x + 1 \) meters (one more than twice the breadth).
2. **Write the Area Equation**: The area of a rectangle is given by the formula:
\[
...
|
Topper's Solved these Questions
QUADRATIC EQUATIONS
NCERT|Exercise EXERCISE 4.3|11 Videos
QUADRATIC EQUATIONS
NCERT|Exercise EXERCISE 4.2|6 Videos
QUADRATIC EQUATIONS
NCERT|Exercise Solved Examples|18 Videos
PROBABILITY
NCERT|Exercise SOLVED EXAMPLES|13 Videos
REAL NUMBERS
NCERT|Exercise EXERCISE 1.3|3 Videos
Similar Questions
Explore conceptually related problems
Represent the following situations in the form of quadratic equations: (i) The area of a rectangular plot is 528m^(2) . The length of the plot (in metre) is one more than twice its breadth. We need to find the length and breadth of the plot. (ii) The product of two consecutive positive integers is 306. We need to find the integers. (iii) Rohan's mother is 26 years elder than him. The product of their ages (in years) 3 years from now will be 360. We would like to find Rohan's present age. (iv) A train travels a distance of 480 km at a uniform speed.If the speed has been 8kmh^(-1) less, then it would have taken 3 hours more to cover the same distance. We need to find the speed of the train.
Represent the following situations in the form of quadratic equations: The area of a rectangular plot is 528 m^(2) . The length of the plot (in meters) is one more than twice its breadth. We need to find the length and breadth of the plot.
The area of a rectangular plot is 528m^(2). The length of the plot (in metres) is one metre more then twice its breadth.Find the length and the breadth of the plot.
The product of two consecutive positive integers is 306. Find the integers.
The area of a rectangular plot is 528m^(2). The length of the plot (in metres) is one more than twice its breadth.Formulate the quadratic equation to determine the length and breadth of the plot.
Represent the following situations in the form of quadratic equations: Rohan's mother is 26 years older than him. The product of their ages (in years) 3 years from now will be 360. We would like to find Rohan's present age.
Represent the following situations in the form of quadratic equations : The product of two consecutive positive integers is 306. We need to find the integers.
Represent the following situations in the form of quadratic equations: The produt of two consecutive positive integers is 306. We need to find the integers.
The product of two consecutive positive integers is 306. Form the quadratic equation to find the integers,if x denotes the smaller integer.
Sanket purchesed a rectangular plot having area 200m^2 . Length of the plot was 10m more than its breadth. Find the length and breadth of the plot.
