5. Is it possible to design a rectangular park of perimeter 80 m and area 400 m?? If so, find its length and breadth.
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Step-by-step explanation:
Answer
Let the length be l m and the breadth be b m.
Then the area would be lb=400
Perimeter would be 2(l+b)=80
lb=400
⇒2(l+b)=80
⇒l+b=40
∴b=40−l --(1)
Substituting (1) in Area, we get
⇒l(40−l)=400
⇒40l−l
2
=400
⇒l
2
−40l+400=0
⇒(l−20)(l−20)=0
∴l=20
has equal roots, so it is possible to design the rectangle of given parameters.
⇒b=40−20=20
We now know that the length of the park is 20 m and the breadth of the park is also 20 m.
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