Question

The perimeter of a rectangular field is 82 m and its area is 400 m². Find the breadth of the rectangle.

Answer 1

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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Answer 2

perimeter of rectangle = 2( l +b ) = 82 m

=> l + b = 41 m --------------1

area = l × b = 400

=> lb = 400

( l - b )² = ( l +b )² - 4lb

=> ( l - b )² =( 41 )² -4 × 400

=> ( l - b )² = 1681 -1600

=> ( l - b )² = 81

=> ( l - b ) = 9 ------------------2

add 1 and 2 , we get

=> l + b = 41 m --------------1
=> ( l - b ) = 9 ----------------2
----------------------------------------------
=> 2l = 50
=> l = 25m

=> b = 41 - 25 = 16 m