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The Equations of Two Sides of a Square Are 5x − 12y − 65 = 0 and 5x − 12y + 26 = 0. Find the Area of the Square. - Mathematics

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प्रश्न

The equations of two sides of a square are 5x − 12y − 65 = 0 and 5x − 12y + 26 = 0. Find the area of the square.

 

उत्तर

The sides of a square are
5x − 12y − 65 = 0            ... (1)
5x − 12y + 26 = 0            ... (2)
We observe that lines (1) and (2) are parallel. So, the distance between them will give the length of the side of the square.
Let d be the distance between the given lines.

\[\Rightarrow d = \left| \frac{- 65 - 26}{\sqrt{5^2 + \left( - 12 \right)^2}} \right| = \frac{91}{13} = 7\]
∴ Area of the square = 72
                                   = 49 square units

 

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अध्याय 23: The straight lines - Exercise 23.16 [पृष्ठ ११४]

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आरडी शर्मा Mathematics [English] Class 11
अध्याय 23 The straight lines
Exercise 23.16 | Q 2 | पृष्ठ ११४

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