Question

The perimeter of a rectangular field is 82 cm and its area is 400 cm^2. Then the breadth of the rectangle in cm

Answer 1

16 cm OR 25 cm

Step-by-step explanation:

We know that Perimeter of a

rectangle = 2(l+b)

&, it's area = l × b

Given , Perimeter = 82 cm

& Area = 400 cm²

Also,

Perimeter = 2( l+b)

=> 2(l + b) = 82 cm

=> l + b = 82 cm/2 = 41 cm

=> l = 41 cm - b

&

Area = l × b

=> l × b = 400 cm²

=> (41-b) × b = 400 cm² { since, l = 41-b}

=> 41 b - b² = 400 cm²

=> -b² + 41b - 400 cm² = 0

Factorising middle term ,

b² - 41b + 400

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

Therefore, b = 16 cm or b = 25 cm

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