Q. 44.0( 5 Votes )

# A rectangular garden is designed such that the length of the garden is twice its breadth and the area of the garden is 800 m^{2}. Find the length of the garden.

Answer :

Let the breadth of garden be b

Thus length = 2b

Area of garden = 800 m^{2}

Area = length × breadth

⇒ 800 = 2b × b

⇒ 800 = 2b^{2}

⇒ b^{2} = 400

⇒ b^{2} = 20^{2}

⇒ b^{2} – 20^{2} = 0

Using identity (a + b)(a – b) = a^{2} – b^{2}

⇒ (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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