Question

Represent the given situation in the form of a quadratic equation: The length of a rectangular park (in metres) is one more than twice its breadth and its area is $528m$${}^2$.

Answer 1

Let the breadth of rectangular park be $x$.

It is given that the length of the park is one more than twice its breadth, therefore, the length of the rectangular park is $(2x+1)$.

Since the area of rectangle with length $l$ and breadth $b$ is $(l\times b)$ and here the area is $528$ m${}^2$, therefore,

$528=(2x+1)x\Rightarrow (2x+1)x=528\Rightarrow 2x^2+x=528\Rightarrow 2x^2+x-528=0$

We know that the general form of quadratic equation is $a{x}^2+bx+c=0$ and the equation $2x^2+x-528=0$ is of the form $a{x}^2+bx+c=0$.

Hence, the equation $2x^2+x-528=0$ is a quadratic equation representation of the given statement.