Question

At is posible to design a rectangular park of perimeter
80 and area 400 m²? if so find its length and breadth​

Answer 1

Answer:

$\displaystyle\huge\red{\underline{\underline{AnSWer}}}$

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−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

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

Answer 2

$\huge{\mathfrak{\purple{ANSWER}}}$

Let ,

length = l

breadth = b

Then ,

$\pink{ Area = l×b}$

.°. Area = 400

And,

$\orange{Perimeter = 2(l+b)}$

⇒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

⇒b=40−20=20

Hence, the length of the park is 20 m and the breadth of the park is 20 m.

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