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

Advertisement Remove all ads

#### 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

Is there an error in this question or solution?

Advertisement Remove all ads

#### APPEARS IN

Advertisement Remove all ads

Advertisement Remove all ads