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is it possible to make a rectangular park of perimeter 80 m and ate a 400 m²?​

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YUMEKOOO88IN

Is it possible to design a rectangular park of perimeter 80 m and area 400 m2?

  • If so, find its length and breadth.So, the given quadratic equation has equal roots and hence it is possible to design a rectangular park.

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AGBOIIIN

QUADRATIC EQUATIONS

Question:

  • is it possible to make a rectangular park of perimeter 80 m and ate a 400 m²?

Remember:

P = 2(L+W)

A = LW

SOLUTION

Perimeter

  • 2(L+W) = 80
  • L+W = 80 ÷ 2
  • L+W = 40

Area

  • LW = 400
  • L = 400/W

Now, If the roots of the quadratic equation will not be negative then it is possible.

Substituting the value of L

  • L+W = 40
  • 400/w + w = 40
  • w(400/w + w) = w(40)
  • 400 + w² = 40w
  • w²-40w+400 = 0
  • (w-20)(w-20)= 0
  • w-20 = 0 , w-20=0
  • w=20 , w = 20

====================================

Checking:

P = 2(L+W)

= 2(20+20)

= 2(40)

= 80 ✔️

A = LW

= 20(20)

= 400 ✔️

====================================

ANSWER

  • YES , it is possible even if it is a square because rectangles can also be squares but squares cannot be rectangles.

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