Question

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

Answer 1

Answer:

yes

Step-by-step explanation:

2 (length +breadth)=80

if x= length ,y=breadth

2 (x+y)=80

x+y=40

x=40-y ____(1)

x×y=400

then value of (1)put

(40-y)×y=400

40y-y^2=400

y^2-40y+400=0

y=10 or40

x=40 or 10

hence the length of rectangular is x=40 when y=10 and x=10 when y=40

breadth y=10 when x=40

and y=40 when x=10

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Answer 2

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Let the length and breadth of a rectangular park are x and y m . respectively.

Accordingly :-

2.(x+y)= 80. , or x. + y = 40………….(1)

, x.y = 400………….(2)

Putting y = 40 - x from eqn. (1) in eqn. (2).

x.(40-x) = 400.

or, x^2 - 40x +400 = 0

or, (x-20)^2. = 0.

or, x-20 = 0. =>. x= 20 m. , but y = 40 - x = 40–20 = 20 m.

Thus , length = breadth = 20 meters.