Is it possible to design a rectangular park of perimeter 80 m and area 400 m2? If so, find its length and breadth.

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Is it possible to design a rectangular park of perimeter 80 m and area 400 m2? If so, find its length and breadth.

Is it possible to design a rectangular park of perimeter 80 m and area 400 m²? If so, find its length and breadth.

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Salim Ahmed Kawsar · Answer 1 · Feb 05, 2023 15:29:48

Solution:

Length = l

Breadth = b

Perimeter = 2(L+b) = 80

=> l+b = 40 .......... (eq 1)

Area = lb = 400 ........... (eq 2)

=> (l+b)²= (l-b)² + 4lb

=> 40² = (l-b)²+ 4 x 400 [From eqn 1 & 2)

=> 1600 = (l-b)² + 1600

=> l-b = 0 .................... (eq 3)

L+b = 40

L-b = 0

2L = 40 => L = 20.

If L=20, then B=20

So, yes ! We can construct a rectangular park of this length which is a square. Square is a Rectangle.

Salim Ahmed Kawsar · Answer 2 · Feb 05, 2023 15:29:48

let length=xm
let breath=ym
According to Question
Perimeter=80m
2(x+y)=80
x+y=40
y=40-x
area=400m
xy=400
x(40-x)=400
`x^2-40x+400=0`
Solving this
x=20m
putting this value in equation 1
y=20m

Is it possible to design a rectangular park of perimeter 80 m and area 400 m2? If so, find its length and breadth.

2 Answers