Question

Is it possible to design a rectangular park of perimeter 80m and area 400m if so find its length and breadth?

Answer 1

let consider, "x" & "y" are the length and breadth of the rectangular park.
perimeter, 2(x+y)= 80..........(i)
area, x*y = 400
or, x= 400/ y................(ii)
putting the value of "x" in equation (i),we get,
2(x+y)= 80
or, x+y = 40
or, (400/y) + y = 40
or, 400 + y^2 = 40*y
or, y^2 - 40*y +400 =0
or, y^2 - 2*y*20 + 20^2 =0
or, (y - 20)^2=0
or, y = 20 m
putting "y" value in equation (ii),we get,
x = 400/ y
or, x = 400/ 20
or, x= 20 m
length & breadth of the rectangular park are 20 m , 20 m respectively..

Answer 2

$\bf\huge\boxed{\boxed{\bf\huge\:Hello\:Mate}}}$

$\bf\huge Let\: length\: be\: x\: metres\: and\: breadth\: be\: y\: metres$

$\bf\huge Perimeter = 80m$

$\bf\huge => 2(x + y) = 80$

$\bf\huge => x + y = 40 (Eqn1)$

$\bf\huge Area = 400 m$

$\bf\huge => xy = 400$

$\bf\huge => x(40 - x) = 400 (From Eqn 1)$

$\bf\huge =>40x - x^2 = 400$

$\bf\huge => x^2 - 40x + 400 = 0$

$\bf\huge Hence\: , a = 1 , \:b = -40 \:and\: c = 400$

$\bf\huge => D = b^2 - 4ac$

$\bf\huge => D = (-40)^2 - 4\times 1 \times 400$

$\bf\huge => D = 1600 - 1600 = 0$

$\bf\huge Equation\: has\: equal\: roots$

$\bf\huge Length \:and\: Breadth$

$\bf\huge => x^2 - 40x + 400 = 0$

$\bf\huge => (x - 20)^2 = 0$

$\bf\huge => x = 20 , 20$

$\bf\huge Length = 20m\: and\: Breadth = 20m$

$\bf\huge Hence\:Design\: is\: Possible$

$\bf\huge\boxed{\boxed{\:Regards=\:Yash\:Raj}}}$