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Some Question and Their Alternative Answer Are Given. Select the Correct Alternative. Find Perimeter of a Square If Its Diagonal is 10 √ 2 - Geometry

MCQ

Some question and their alternative answer are given. Select the correct alternative.

Find perimeter of a square if its diagonal is \[10\sqrt{2}\]

Options

  • 10 cm 

  •  \[40\sqrt{2}\]cm 

  • 20 cm 

  • 40 cm

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Solution

It is given that ABCD is a square.

∴ AB = BC = CD = DA = x (say)

According to Pythagoras theorem, in ∆ABD

\[{\text{AB}}^2 + {\text{AD}}^2 = {\text{BD}}^2 \]
\[ \Rightarrow x^2 + x^2 = \left( 10\sqrt{2} \right)^2 \]
\[ \Rightarrow 2 x^2 = 200\]
\[ \Rightarrow x^2 = 100\]
\[ \Rightarrow x = \sqrt{100}\]
\[ \Rightarrow x = 10 \text{cm}\]

Hence, the side of the square is 10 cm.

Now,
Perimeter of a square = \[4 \times \left( side \right)\]

=\[4 \times x\]

=\[4 \times 10\]

=\[40\]

Hence, the correct option is 40 cm.

Concept: Apollonius Theorem
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APPEARS IN

Balbharati Mathematics 2 Geometry 10th Standard SSC Maharashtra State Board
Chapter 2 Pythagoras Theorem
Problem Set 2 | Q 1.5 | Page 43
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