# 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.

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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.

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.

Last updated date: 18th Sep 2023

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