Question

Represent the following situations in the form of quadratic equations : (i) The area of a rectangalar plot is 528m². 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.

Answer 1

To represent the given situation in the form of a quadratic equation, assume that the breadth of the plot is 'x' meters. The length of the plot can be expressed as (2x + 1) meters. The quadratic equation representing the situation is 2x^2 + x - 528 = 0.

Step-by-step explanation:

To represent the given situation in the form of a quadratic equation, let's assume that the breadth of the plot is 'x' meters. According to the problem, the length of the plot is one more than twice its breadth, so the length can be expressed as (2x + 1) meters.

The area of a rectangle is given by multiplying its length and breadth. So, the quadratic equation representing the situation is:

Area = Length x Breadth

528 = (2x + 1) x x

528 = 2x^2 + x

2x^2 + x - 528 = 0

This is the quadratic equation representing the given situation. We can use this equation to find the length and breadth of the plot by solving it either by factoring, completing the square, or using the quadratic formula.