Question

the area and perimeter of a rectangular field is 600 sqm and 10 m find the length and breadth of the field

Answer 1

Basic Knowledge: -)

Area of rectangular field with length x and breadth y is given by

$Area = x \times y$

And

Perimeter of rectangular field with length x and breadth y is given by

$Perimeter = 2(x + y)$

Procedure :-)

To solve this question we will put value of area and perimeter in about two relations to get two equations in x and y.

After solving these two equations we will get values of x and y which will be the required length and breadth of the rectangular field .

( but during solution we will observe that there will be no possible value of x and y for the given condition)

Solution :-)

$x \times y = 600 \: \: \: ..(i) \\ \\ \\and \\ \\ 2(x + y) = 10$

$x + y = 5 \\ \\ \implies y = 5 - x \: \: \: \: ..(ii)$

On putting (ii) in (i)

We get

$x(5 - x) = 600 \\ \\ {x}^{2} - 5x + 600 = 0$

From Here

We will not get any real root.

As

${( - 5)}^{2} - 4 \times 1 \times 600 < 0 \\ \\ i.e. \\ \\ D < 0$

So,

No rectangular field can exist having area 600 sq m and perimeter 10m .

Answer 2

Answer:

$2(l + b) = 10 \\ \\ l + b = 5 \\ \\ l = 5 - b \: \: \: \: \: \:.. (1) \\ \\ l \times b = 600 \: \: \: \: \: \: \: ..(2)$

Put (1) in (2)

$(5 - b) \times b = 600 \\ \\ 5b - {b}^{2} = 600 \\ \\ {b}^{2} - 5 b + 600 = 0$

Here discriminant of the quadratic equation is less than zero

So no real value of l and b can exists.

Mark as brainleist

Thanks

foIIow me as well.