Question

it is possible to design a rectangular park of perimeter 80m and area 400m²? if so, find its length and breadth??​

Answer 1

Answer:

20 m and 20 m.

Step-by-step explanation:

Let the length of that rectangle be a and breadth be b.{ units are ignored in calculation }

       According to the question:

     Perimeter of rectangle is 80 m

        ⇒ 2( a + b ) = 80 m

        ⇒ a + b = 40  

        ⇒ b = 40 - a           ...( 1 )

Given,

      ⇒ Area = 400

      ⇒ length x breadth = 400

      ⇒ ab = 400

      ⇒ a( 40 - a ) = 400             { from ( 1 ) b = 40 - a }

      ⇒ 40a - a^2 = 400

      ⇒ a^2 - 40a = - 400

      ⇒ a^2 + 400 - 40a = 0

      ⇒ a^2 + 20^2 - 2(20a) = 0

      ⇒ ( a - 20 )^2 = 0            { using a^2 + b^2 - 2ab = ( a - b )^2 }

      ⇒ a - 20 = 0      ⇒ a = 20

Thus,

      Length is 20 m and breadth is 40 - 20 m = 20 m.

Answer 2

Step-by-step explanation:

Aloha !

$\text{ This is Twilight Astro}$ ^_^

perimeter= 80m

2(a+b)=80

a+b=40m

a=40-b

We have ,..

Area= 400m²

a×b=400m²

(40-b)×b=400

40b-b²=400

b²-40b+400=0

b²-2(20b)+20²=0

(b-20)²=0

b-20=0

b=20m

a+b=40

a+20=40

a=20m

Thank you

@ Twilight Astro ✌️☺️♥️