Question 32 - CBSE Class 10 Sample Paper for 2027 Boards - Maths Standard - Solutions of Sample Papers for Class 10 Boards

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Question 32 In a rectangular park measuring 50 m×40 m, the gram panchayat plans to construct a rectangular swimming pool in the middle, surrounded by a uniform width grass strip throughout the park. Find the dimensions of the swimming pool, if the area of the grassy strip is 1184 m^(2). Let’s draw the diagram x x x x 50 m 40 m Here, Length of rectangular park = 50 m Breadth of rectangular park = 40 m Given that swimming pool is constructed in the middle And that there is a uniform width grass strip throughout the park Let Uniform width of grass strip = x m Also, area of the grassy strip is 1184 m^(2), and we need to find dimensions of the swimming pool Now, Length of swimming pool = 50 – x – x = (50 – 2x) m Breadth of swimming pool = 40 – x – x = (40 – 2x) m Given Area of grass strip = 1184 m^(2) Area of rectangular park – Area of swimming pool = 1184 50 × 40 – (50 – 2x) × (40 – 2x) = 1184 2000 – [50 × (40 – 2x) – 2x (40 – 2x)] = 1184 2000 – [2000 – 100x – 80x + 4x^(2)] = 1184 2000 – [2000 – 180x + 4x^(2)] = 1184 2000 – 2000 + 180x – 4x2 = 1184 –4x^(2) + 180x = 1184 0 = 4x^(2) – 180x – 1184 4x^(2) – 180x + 1184 = 0 4(x^(2) – (180)/(4)x + (1184)/(4)) = 0 x^(2) – 45x + 296 = 0 Solving by splitting the middle term So, our equation becomes x^(2) – 37x – 8x – 296 = 0 x (x – 37) – 8 (x – 37) = 0 (x – 8) (x – 37) = 0 So, x = 8, x = 37 Splitting the middle term method We need to find two numbers where Sum = –45 Product = 1 × 296= 296 Since sum is negative and product is negative. Both numbers are negative | Sum | Product | | –45 296 –37 & –8 We need to find length and breadth of swimming pool Now, Length of swimming pool = (50 – 2x) m Breadth of swimming pool = (40 – 2x) m So, x = 37 is not possible as our length & breadth will be negative then Thus, x = 8 So, Length of swimming pool = (50 – 2x) = 50 – 2 × 8 = 50 – 16 = 34 m Breadth of swimming pool = (40 – 2x) = 40 – 2 × 8 = 40 – 16 = 24 m