Question

19. Determine the dimensions of a rectangular park whose perimeter is 80 m and area 400 sq m.

Answer 1

Answer:

L×B=400. eq1

2(L+B)=80

(L+B)=40

L=40-b

put this value in equation 1

(40-b)b=400

40b-b2=400

b2-40b+400=0

b2-20b -20b+400=0

b(b-20)-20(b-20)=0

(b-20)(b-20)=0

b=20

L=40-b

L=40-20

L=20

Answer 2

The dimensions of the rectangular park is $20\times 20$ m.

Step-by-step explanation:

Given : A rectangular park whose perimeter is 80 m and area 400 sq m.

To find : Determine the dimensions of a rectangular park ?

Solution :

Let the length be 'l' and breadth be 'b'.

The perimeter of the rectangular park is $P=2(l+b)$

i.e. $2(l+b)=80$ ....(1)

The area of the rectangular park is $A=l\times b$

i.e. $l\times b=400$ ....(2)

Solving (1) and (2),

Substitute 'b' from (2) in (1),

$2(l+\frac{400}{l})=80$

$\frac{l^2+400}{l}=40$

$l^2-40l+400=0$

$l^2-20l-20l+400=0$

$l(l-20)-20(l-20)=0$

$(l-20)(l-20)=0$

$l=20$

Length is 20 m.

Substitute in (2),

$20\times b=400$

$b=\frac{400}{20}$

$b=20$

Breadth is 20 m.

The dimensions of the rectangular park is $20\times 20$ m.

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