Question:is it possible to design a rectangular mango grove whose length is twice it's breadth and area is 800 m2 ? If so ,find its length and breadth.?

Question

Answer

It is given that length is twice of breadth,
so, let us take breadth=b=x m,
then, length=l=2(x)m,
we know that area of a rectangle=l×b,
or, 800=2x(x){ area of the rectangle=800m^2-- (given)},
or, 800/2=x^2,
400=x^2,
x=√400=20,
or, b=20m,
l=2x=2(20)=40m so ,it is possible to design a rectangular mango grove whose length is twice its breadth.

Answer

Answer

Yes , it is possible
Let breadth = x
Length = 2x
area = length × metre
800 = x × 2x
2x^2 = 800
x^2 = 800/2
x^2 = 400
x = root under 400
x = 20 meter
Hence, breadth = 20 m
length = 20 × 2 = 40 m

Answer

Analysis

To solve this problem, we need to find the length and breadth of a rectangular mango grove. We are given that the length is twice the breadth and the area is 800 m². Let's break down the problem into smaller steps.

Solution

Step 1: Assign variables to the length and breadth of the rectangular mango grove.
Let's assume the breadth of the grove is 'x' meters. Since the length is twice the breadth, we can assign the length as '2x' meters.

Step 2: Write the formula to calculate the area of a rectangle.
The area of a rectangle can be calculated by multiplying the length and breadth. Therefore, the area of the mango grove is given by the formula:
Area = Length × Breadth

Step 3: Substitute the given values into the formula.
We are given that the area is 800 m². Substituting the values into the formula, we get:
800 = (2x) × x

Step 4: Simplify the equation.
To simplify the equation, we can multiply the terms inside the parentheses:
800 = 2x²

Step 5: Solve the equation.
To solve the equation, we need to isolate the variable. We can divide both sides of the equation by 2:
400 = x²

Step 6: Take the square root of both sides.
Taking the square root of both sides of the equation gives us:
x = √400

Step 7: Simplify the square root.
The square root of 400 is 20, so:
x = 20

Step 8: Calculate the length.
Since the length is twice the breadth, we can substitute the value of x into the equation:
Length = 2x = 2(20) = 40

Conclusion

Therefore, the length of the rectangular mango grove is 40 meters and the breadth is 20 meters. This design satisfies the given conditions of having a length twice the breadth and an area of 800 m².

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