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Question

# A rectangular playground is 420 sq.m. If its length is increases by 7 m and breadth is decreased by 5 metres, the area remains the same. Find the length and breadth of the playground?

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Solution

## Let the length of the rectangular playground is x m. Then, its breadth is $\frac{420}{x}$ m ,as area is given 420 m2. Thus, by the given condition, we get $\left(x+7\right)\left(\frac{420}{x}-5\right)=420\phantom{\rule{0ex}{0ex}}⇒\left(x+7\right)\left(420-5x\right)=420x$ $⇒$ 420x –5x2 + 2940 –35x = 420x $⇒$ 5x2 +35x – 2940 = 0 $⇒$ 5(x2 + 7x – 588) = 0 $⇒$ x2 + 7x – 588 = 0 On splitting the middle term 7x as 28x – 21x, we get $⇒$ x2 + 28x – 21x – 588 = 0 $⇒$ x(x + 28) – 21(x + 28) = 0 $⇒$ (x + 28)(x – 21) = 0 $⇒$ x + 28 = 0 or x – 21 = 0 $⇒$ x = –28 or x = 21 Since, the length of the playground cannot be negative, so we get x = 21 Thus, the length of the playground is x = 21 m and the breadth of the playground is $\frac{420}{x}=\frac{420}{21}=20\mathrm{m}.$

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