# 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.

Last updated date: 26th Mar 2023

•

Total views: 309.3k

•

Views today: 2.86k

Answer

Verified

309.3k+ views

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.

Recently Updated Pages

If a spring has a period T and is cut into the n equal class 11 physics CBSE

A planet moves around the sun in nearly circular orbit class 11 physics CBSE

In any triangle AB2 BC4 CA3 and D is the midpoint of class 11 maths JEE_Main

In a Delta ABC 2asin dfracAB+C2 is equal to IIT Screening class 11 maths JEE_Main

If in aDelta ABCangle A 45circ angle C 60circ then class 11 maths JEE_Main

If in a triangle rmABC side a sqrt 3 + 1rmcm and angle class 11 maths JEE_Main

Trending doubts

Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Write a letter to the principal requesting him to grant class 10 english CBSE

List out three methods of soil conservation

Epipetalous and syngenesious stamens occur in aSolanaceae class 11 biology CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

A Short Paragraph on our Country India