Q5 of 83 Page 88

Perimeter of a rectangular garden is 360 m and its area is 8000 m2. Find the length of the garden and also find its breadth. (The length is greater than the breadth)

Let l be length of rectangle and b be breadth of rectangular garden


Perimeter = 360 m


Perimeter = 2 × (length + breadth) = 2(l + b)


⇒ 2(l + b) = 360


⇒ l + b = 180


⇒ l = 180 – b …(i)


Area = 8000


Area = length × breadth


⇒ 8000 = lb


Using (i)


⇒ 8000 = (180 – b) × b


⇒ 8000 = 180b – b2


⇒ b2 – 180b + 8000 = 0


⇒ b2 – 100b – 80b + 8000 = 0


taking b common from first two terms and – 80 common from next two


⇒ b2 – 100b – 80b + 8000 = 0


⇒ b(b – 100) – 80(b – 100) = 0


⇒ (b – 80)(b – 100) = 0


⇒ (b – 80) = 0 or (b – 100) = 0


b = 80 m because it is given that breadth is smaller than length


using (i) l = 180 – 80 = 100 m


Therefore, length of garden is 100 m and breadth is 80 m


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