Question

Quadratic equations have many aspects in real life. Quadratic equations are very useful while calculating areas of a room, box, perimeter a plot of land etc. For example. Rajuvinder need to make a top of a study table whose length is 1.5 m longer than its breadth. He has various questions in his mind. Help him to answer the questions.(5M)

(a) If Rajuvinder has 3m2 of plywood. He used it to make a top of a study table whose length is 1.5 m longer than its breadth. Represent this situation in form of quadratic equation.
(b) What are the dimensions of top of the study table?
(c) If Rajuvinder keeps the length and breadth of top of study table equal then what is the quadratic equation representing this situation?
(d) What are the dimensions of square shaped study table?
(e) In which he has more area of top of study table?​

Answer 1

To represent the situation in the form of a quadratic equation, let the breadth be 'x' meters. The length is 1.5 meters longer than the breadth. The quadratic equation is x(x + 1.5) = 3. The dimensions of the table can be found by solving the quadratic equation.

Step-by-step explanation:

To represent the given situation in the form of a quadratic equation, let's assume the breadth of the top of the study table as 'x' meters. According to the given information, the length of the top is 1.5 meters longer than the breadth, so the length would be 'x + 1.5' meters. The area of the study table's top is given as 3 square meters. Using the formula for the area of a rectangle (length × breadth), we can write the quadratic equation as:

x(x + 1.5) = 3

Simplifying the equation:

x^2 + 1.5x - 3 = 0

This is the quadratic equation that represents the given situation.

To find the dimensions of the top of the study table, we can solve the quadratic equation. The solutions of the equation will give us the values of 'x', which represents the breadth. By substituting the value of 'x' in the equation, we can find the corresponding length.

If Rajuvinder keeps the length and breadth of the top of the study table equal, it means both dimensions will be 'x'. So the quadratic equation representing this situation would be:

x(x) = 3

Simplifying the equation:

x^2 = 3

This is the quadratic equation representing the situation where the length and breadth are equal.

To find the dimensions of a square-shaped study table, we can set the length and breadth equal, so x = x + 1.5. Simplifying this equation, we get 1.5 = 0, which is not a valid equation. Therefore, a square-shaped study table cannot be formed with the given information.

To determine which shape of the study table has a greater area, we can compare the area given by the quadratic equation x(x+1.5) = 3 with the area given by the quadratic equation x(x) = 3. By solving these equations, we can find the respective areas and compare them to determine which is larger.