Question

If the perimeter is 82 meter and its area is 400 sq m then what is its breadth ?

Answer 1

perimeter of rectangle=2*(l+b)
82=2*(l+b)
82/2=l+b
41=l+b
41-l=b
area of rectangle=l*b
400=l*b
400/l=b
400/l=41-l
400=41l-l^2
l^2-41l+400=0
l^2-25l-16l+400=0
l(l-25)-16(l-25)=0
(l-25)(l-16)=0
l=16 or 25
then b=25 or 16
anything you can put the value of b

Answer 2

SOLUTION :  

Given :  

Perimeter of a rectangular field = 82 m

Area of a rectangular field = 400 m²

Let the breadth of a rectangle be 'b’ m.

Perimeter of a rectangle = 2(l + b)

82 = 2(l + b)

82/2 = (l + b)

l + b = 41  

Length,l = 41 - b …………(1)

Area of a rectangle  = l × b

400 = (41 - b) b

[From eq 1]

400 = 41b - b²

b² - 41b + 400 = 0

b² - 25b - 16b + 400 = 0

[By middle term splitting]

b(b - 25) - 16(b - 25) = 0

(b - 25) (b - 16) = 0

(b - 25) = 0  or  (b - 16) = 0

b = 25 or b = 16  

If breadth,b = 25 , then length, l = 41 - b  

l = 41 - 25 = 16 m

If breadth,b = 16 , then length, l = 41 - b  

l = 41 - 16 = 25 m

Since, length is more than breadth  

Therefore , breadth, b = 16 m

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