# Ex.4.4 Q3 Quadratic Equations Solutions - NCERT Maths Class 10

## Question

Is it possible to design a rectangular mango groove whose length is twice its breadth, and the area is $$800\,\rm{m}^².$$ If so, find its length and breadth.

Video Solution
Ex 4.4 | Question 3

## Text Solution

What is known?

i) Mango groove length is twice its breadth.

ii) Area $$=800\,\rm{m}^².$$

What is Unknown?

Finding the possibility of mango groove and if possible length and breadth.

Reasoning:

Let the breadth of rectangle $$x\,\rm{ m.}$$

$$\text {Length}= 2x\,\rm{m}$$

$$\text{Area}= \rm{Length} × \rm{Breadth}$$

Steps:

$$\text{Area}=\rm{ Length} × \rm{Breadth}$$

\begin{align}800 &= x \times 2x\\2{x^2} &= 800\\{x^2} &= \frac{{800}}{2}\\{x^2} &= 400\\ {x^2} - 400 &= 0\end{align}

Discriminant of a quadratic equation is $$b² - 4ac.$$ Comparing $${x^2} - 400 = 0$$ with $$ax^{2}+bx+c=0$$:

$$a = 1,\, b = 0, \,c = - 400$$

\begin{align}{b^2} - 4ac &= {{(0)}^2} - 4(1)( - 400)|\\ &= + 1600 > 0 \end{align}

$$\therefore$$ Yes, it is possible to design a mango groove.

\begin{align}{x^2} - 400 &= 0\\{x^2} &= 400\\x\, &= \pm 20\end{align}

Value of $$x$$ can’t be negative value as it represents the breadth of the rectangle.

$$\therefore\; x = 20\,\rm{m}$$

So, yes, possible to design the mango groove

Length $$= 2x = 2(20) = 40\,\rm{m}$$

Breadth $$= x = 20\,\rm{m}$$

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