Find the Side and Perimeter of a Square Whose Diagonal is 10 Cm. - Geometry Mathematics 2

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Find the side and perimeter of a square whose diagonal is 10 cm ?

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Solution

It is given that ABCD is a square.
∴ AB = BC = CD = DA = a (say)
According to Pythagoras theorem, in ∆ABD

\[{AB}^2 + {AD}^2 = {BD}^2 \]
\[ \Rightarrow a^2 + a^2 = {10}^2 \]
\[ \Rightarrow 2 a^2 = 100\]
\[ \Rightarrow a^2 = 50\]
\[ \Rightarrow a = \sqrt{50}\]
\[ \Rightarrow a = 5\sqrt{2} cm\]

Hence, the side of the square is 5\[\sqrt{2}\] cm.

Now,
Perimeter of a square = \[4 \times \left( side \right)\]
= \[4 \times a\]
= \[4 \times 5\sqrt{2}\]
= \[20\sqrt{2}\] cm
Hence, the perimeter of the square is 20 \[\sqrt{2}\] cm
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Chapter 2: Pythagoras Theorem - Practice Set 2.1 [Page 39]

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Balbharati Mathematics 2 Geometry 10th Standard SSC Maharashtra State Board
Chapter 2 Pythagoras Theorem
Practice Set 2.1 | Q 6 | Page 39

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