#### Question

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

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

10 cm

\[40\sqrt{2}\]cm

20 cm

40 cm

#### 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.

Is there an error in this question or solution?

Solution Some Question and Their Alternative Answer Are Given. Select the Correct Alternative. Find Perimeter of a Square If Its Diagonal is 10 √ 2 Concept: Apollonius Theorem.