Question

3. Is it possible to design a rectangular mango grove whose length is twice its breadth,
and the area is 800 m²? If so, find its length and breadth.​

Answer 1

Answer :

• Breadth is 20 m and length is 40m

Given :

• Length is twice its breadth
• Area is 800m²

To find :

• Length
• Breadth

Solution :

• Let the breadth be x
• Let the length be 2x

As we know that,

• Area of rectangle = l × b

Where,l is length 2x and b is breadth x

⇢ Area of rectangle = length × breadth

⇢ 800 = 2x × x

⇢ 800 = 2x²

⇢ x² = 800/2

⇢ x² = 400

⇢ x = ±√400

⇢ x = ± 20

Then , x = 20 or x = - 20

• x cannot be negative so, x = 20

Now we have to find the length and breadth:

• Breadth = x = 20 m
• Length = 2x = 2(20) = 40 m

Hence, Breadth is 20 m and length is 40m

More Explanation :

• Perimeter of rectangle = 2(l + b)
• Area of rectangle = length × breadth
• Diagonal = √(l² + b²)
• Where , l is length and b is breadth

Answer 2

A N S W E R :

• The Breadth is 20m

• The Length is 40m

Given :-

• Length is twice its breadth
• Area is 800 m²

To find :-

• Find Length ?
• Find Breadth ?

★ $\large\underline{\frak{As ~we~ know ~that,}}$

$\large\dag$ Formula Used :

• $\boxed{\bf{Area~of~rectangle~=~Length~×~Breadth}}$

Solution :-

• Let the breadth be x
• Let the length be 2x

• L is the length 2x and B is the breadth x

:$\implies$Area of reactangle = Length × Breadth

$~~~~~$:$\implies$800 = 2x × x

$~~~~~~~~~~$:$\implies$800 = 2x²

$~~~~~~~~~~~~~~~$:$\implies$x² = $\large{\sf{\frac{800}{2}}}$

$~~~~~~~~~~~~~~~~~~~~$:$\implies$x² = ${\cancel{\dfrac{800}{2}}}$

$~~~~~~~~~~~~~~~~~~~~~~~~~$:$\implies$x² = 400

$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~$:$\implies$x = ${\sf{±√400}}$

$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~$:$\implies$${\underline{\boxed{\pink{\frak{x~=~±20}}}}}$★

$\large\dashrightarrow$x = 20

$~~~~~$$\large\dashrightarrow$x = -20

$\therefore$ Hence,

• x cannot be negative

• x = $\large\underline{\rm{20}}$

V E R I F I C A T I O N :

• Find the length and breadth :

• The Breadth = x = 20m

• The Length = 2x = 2(40) = 40m

$\large\dag$ Hence Verified !!

• The Breadth is = $\large\underline{\rm{20m}}$

• The Length is = $\large\underline{\rm{40m}}$