REAL PROBLEMS AND EXERCISE 2 6 - PUNJAB-CURRICULUM-AND-TEXTBOOK-BOARD-PCTB / 10TH-CLASS / MATHEMATICS / MATHEMATICS-10-10TH-CLASS-NBF-2024 / QUADRATIC-EQUATIONS / REAL-PROBLEMS-AND-EXERCISE-2-6

Real Problems Involving Quadratic Equations

There are many problems which lead to quadratic equations. To form an equation, we consider symbols for unknown quantities in the problems.

In order to solve problems, we must have

(i) Suppose the unknown quantities to be x or y

(ii) Translate the problem into symbols and form the equation satisfying the conditions.

The method of solving the problem will be illustrated through the following examples.

Example: The length of a room is 3 meters greater than its breadth. If the area of the room is 180 square meters, find length and breadth of the room.

Solution: Let the breadth of room $= x$ metres and the length of room $= x + 3$ metres

Area of the room $= x(x + 3)$ square metres

By the conditions of the equation

x (x + 3) = 180 o r x^{2} + 3 x - 180 = 0

(x + 15) (x - 12) = 0 o r x = - 15, x = 12

As breadth cannot be negative, therefore, we take $x = 12$

L e n g t h = x + 3 = 12 + 3 = 15

Breadth of the room $= 12m$ and length of room $= 15m$

1. Product of two consecutive positive even numbers is 120. Find the numbers.

Real Problems and Exercise 2.6

Real Problems Involving Quadratic Equations

Solution: