Question

If the length of the park is given as 8 metres more than its breadth. If the area of the park is given as $240{m^2}$, then find the length and breadth of the park.

Answer 1

Hint- Since the length and breadth of a park are given, make use of the formula of area of a rectangle and solve this problem.

The values of length and breadth of the park are unknown
Consider the breadth of the park=x metres
Length of the park is given as 8 metres more than its breadth, so length=x+8 metres
The area of the rectangle is given by the formula Area=$Length \times Breadth$
Area is given as =$240{m^2}$
Lets substitute the values in the formula,
So, we get 240=$x \times (x + 8)$
On multiplying the terms in RHS and shifting 240 to the RHS we get
$ \Rightarrow {x^2} + 8x - 240 = 0$
This is in the form of a quadratic equation, so lets factorise by splitting the middle term and solve it
$\begin{gathered}
   \Rightarrow {x^2} + 20x - 12x - 240 = 0 \\
   \Rightarrow x(x + 20) - 12(x + 20) = 0 \\
   \Rightarrow (x - 12)(x - 20) = 0 \\
   \Rightarrow x = 12(\because x \ne - 20) \\
    \\
\end{gathered} $
Therefore we get the value of x=12 metres
But x is nothing but equal to the breadth of the park, and length of the park=x+8
We get the breadth of the park=12 metres
Length of the park =x+8=12+8=20 metres

Note : Always take the positive value in the quadratic equation when you solve, since the
 value of a measurement(length or breadth) cannot be negative, also make sure to not only to find the value of x, but also the value of x+8 which will give us the length of the park.