Question

Perimeter of rectangle is 82 cm and its area is 400 sq m find length of rectangle

Answer 1

The perimeter of the rectangle : 2(L+B) = 82 or L + B = 41 …(1)

LB = 400 …(2), or

(41-B)B=400, or

B^2–41B-400 = 0

B1 = [41+(41^2–1600)^0.5]/2 = [41+9]/2 = 25, No admissible as L becomes 16<B

B2 = [41-(41^2–1600)^0.5]/2 = [41-9]/2 = 16 m

Hence the breadth is 16m and the length is 25 m.

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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