Question

is it possible to design a rectangular mango grove whose length is twice its breath and the area is 800 m square ? if find its length and breadth.

Answer 1

It's possible.
Let x = width of the grove
Then
2x = length
:
Area = L * W:
x(2x) = 800
2x^2 = 800
x^2 = 800/2
x^2 = 400
x = Sqrt(400)
x = 20 m by 40 m
:
:
b>
The sum of the ages of two friends is 20 years. Four years ago, the product of their ages in years was 48. Determine their present ages.
:
It would simply things if we let x and y be the ages 4 years ago
Then
(x+4) and (y+4) = ages now
:
Present age sum = 20:
(x+4) + (y+4) = 20
x + y + 8 = 20
x + y = 20 - 8
x + y = 12
y = 12-x
:
Product of age 4 yrs ago
x*y = 48
y = 48/x
Replace y with 12-x
12-x = 48/x
12x - x^2 = 48
-x^2 + 12x - 48 = 0
This equation has no real roots, (discriminant less than 0)
There is no solution
If we plot these equations, you can see they don't intersect
y = 12-x and y = 48/x
:

: 
:
c>
Is it possible to design a rectangular park of perimeter 80 m and 400 m2? If so, find its length and breadth.
:
It is: let the sides = x and y
Perimeter: 2x + 2y = 80
Simplify, divide by 2
x + y = 40
y = (40-x)
:
Area: 
x * y = 400
Replace y with (40-x)
x(40-x) = 400
40x - x^2 = 400
-x^2 + 40x - 400 = 0
Easier to factor if we multiply by -1
x^2 - 40x + 400 = 0
Factor
(x-20)(x-20) = 0
x = 20, 
:
The park will be a square; 20 by 20