Question

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

Answer 1

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➥ Let the length be ℓ m and Breadth be b m.

⇛Then the area will be l × b = 400m²

⇛Perimeter will be 2(l + b) = 80m

→ l × b = 400

→ 2(l + b) = 80

→ l + b = 40

→ b = 40 - l (i)

Substituting (1) in Area, we get;

→ l(40 - l) = 400

→ 40l - l² = 400

→ l² - 40l + 400 = 0

→ (l - 20)(l - 20) = 0

→ l = 20m

→ b = 40 - 20 = 20m

✓ We now know that the length of the park is 20 m and the breadth of the park is also 20 m.

Hope this helps uh! :)

Answer 2

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

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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−l2=400

⇒l2−40l+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

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