Q4 of 83 Page 88

A rectangular garden is designed such that the length of the garden is twice its breadth and the area of the garden is 800 m2. Find the length of the garden.

Let the breadth of garden be b


Thus length = 2b


Area of garden = 800 m2


Area = length × breadth


⇒ 800 = 2b × b


⇒ 800 = 2b2



⇒ b2 = 400


⇒ b2 = 202


⇒ b2 – 202 = 0


Using identity (a + b)(a – b) = a2 – b2


⇒ (b + 20)(b – 20) = 0


⇒ (b + 20) = 0 or (b – 20) = 0


Therefore b = 20 and not – 20 because b cannot be negative as b is breadth of rectangle and length or breadth cannot be negative


Breadth = 20


Therefore length = 2 × 20 = 40


Therefore, length of the garden is 40 m


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