Answer

Verified

450.9k+ views

Hint: Write the equations relating the length and the breadth of the mango grove and then solve for its length and breadth. If the answer is feasible, then, it is possible to design.

Complete step-by-step answer:

Let the length of the mango grove be l and its breath be b.

It is given that the length of the mango grove is twice its breadth, hence, we have the relation:

\[l = 2b.............(1)\]

We know that the area of a rectangular object is a product of its length and breadth. Hence, area if the rectangular mango grove is given as follows:

\[A = lb...........(2)\]

The area of the rectangular mango grove is given as 800 \[{m^2}\]. Therefore, from equation (2), we have:

\[800 = lb\]

Substituting equation (1) into the above equation, we have:

\[800 = (2b)b\]

We know simplify the right-hand side of the equation, to get:

\[800 = 2{b^2}\]

Taking 2 to the other side and dividing with 800, we get 400.

\[400 = {b^2}\]

We know that the square root of 400 is 20. Hence, we have:

\[b = 20\]

Using equation (1), we obtain the length of the grove as:

\[l = 2 \times 20\]

\[l = 40\]

Hence, the length of the grove is 40m and the breadth of the grove is 20m.

It is a feasible solution. Hence, we can design such a mango grove with given conditions.

Hence, the correct answer is option (b).

Note: When taking a square root we get both positive and negative roots, choose only the feasible solution, in this case, breadth and length are positive quantities.

Complete step-by-step answer:

Let the length of the mango grove be l and its breath be b.

It is given that the length of the mango grove is twice its breadth, hence, we have the relation:

\[l = 2b.............(1)\]

We know that the area of a rectangular object is a product of its length and breadth. Hence, area if the rectangular mango grove is given as follows:

\[A = lb...........(2)\]

The area of the rectangular mango grove is given as 800 \[{m^2}\]. Therefore, from equation (2), we have:

\[800 = lb\]

Substituting equation (1) into the above equation, we have:

\[800 = (2b)b\]

We know simplify the right-hand side of the equation, to get:

\[800 = 2{b^2}\]

Taking 2 to the other side and dividing with 800, we get 400.

\[400 = {b^2}\]

We know that the square root of 400 is 20. Hence, we have:

\[b = 20\]

Using equation (1), we obtain the length of the grove as:

\[l = 2 \times 20\]

\[l = 40\]

Hence, the length of the grove is 40m and the breadth of the grove is 20m.

It is a feasible solution. Hence, we can design such a mango grove with given conditions.

Hence, the correct answer is option (b).

Note: When taking a square root we get both positive and negative roots, choose only the feasible solution, in this case, breadth and length are positive quantities.

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Why Are Noble Gases NonReactive class 11 chemistry CBSE

Let X and Y be the sets of all positive divisors of class 11 maths CBSE

Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE

Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE

Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE

Trending doubts

Establish a relation between electric current and drift class 12 physics CBSE

Guru Purnima speech in English in 100 words class 7 english CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Difference Between Plant Cell and Animal Cell

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

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

Copper is not used as potentiometer wire because class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE