Question

the length of diagonal of a rectangular land is 15 mts and the difference of length and breadth is 3 m . calculate the perimeter​

Answer 1

$\huge{\blue{\bold{\underline{\underline{Answer :}}}}}$

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$\large\underline{\green{\bf Given :-}}$

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• The length of diagonal of a rectangular land is 15 m

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• Difference of length and breadth is 3 m

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$\large\underline{\red{\bf To \: Find :-}}$

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• Perimeter of rectangular land

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We know that , in a rectangle

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➠ Diagonal² = Length² + Breadth²

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• Let the length be "l"

• Let the breadth be "b"

• Let the diagonal be "d"

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➠ d² = l² + b² ⚊⚊⚊⚊ ⓵

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Given that diagonal is 15 m

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➨ d = 15 ⚊⚊⚊⚊ ⓶

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Also given that difference of length and breadth is 3 m

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➜ l - b = 3

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➜ l = 3 + b ⚊⚊⚊⚊ ⓷

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Putting equation ⓶ & ⓷ in ⓵

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➜ d² = l² + b²

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➜ 15² = (3 + b)² + b²

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➜ 225 = 3² + b² + 2(3)(b) + b²

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➜ 225 = 9 + 2b² + 6b

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➜ 2b² + 6b = 225 - 9

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➜ 2b² + 6b = 216

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Dividing the above equation be 2

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➜ b² + 3b = 108

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➜ b² + 3b - 108 = 0

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➜ b² + 12b - 9b - 108 = 0

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➜ b(b + 12) -9(b + 12) = 0

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➜ (b + 12)(b - 9) = 0

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• b = -12
• b = 9 ⚊⚊⚊⚊ ⓸

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As breadth can't be negative hence b = 9

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• Hence breadth of rectangle is 9 m

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Putting b = 9 from ⓸ to ⓷

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➜ l = 3 + b

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➜ l = 3 + 9

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➨ l = 12 ⚊⚊⚊⚊ ⓹

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• Hence the length of rectangular land is 12 m

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$\underline{\bold{\texttt{Perimeter of rectangle :}}}$

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➠ 2(l + b) ⚊⚊⚊⚊ ⓺

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Where,

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• l = Length

• b = breadth

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$\underline{\bold{\texttt{Perimeter of given rectangular land :}}}$

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• l = 12 m

• b = 9 m

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Putting these values in ⓺

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➜ 2(l + b)

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➜ 2(12 + 9)

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➜ 2(21)

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➨ 42

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• Hence the perimeter of rectangular land is 42 m

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