Question

Find the side and perimeter of a square whose diagonal is 10 cm.
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Answer 1

Step-by-step explanation:

diagonal = √2× side

therefore,

side = 10/√2

side = 5√2cm ( by rationalising the denominator)

perimeter = 4 × side

= 4 × 5√2

= 20√2 cm

Answer 2

ㅤ$\;\;\underline{\textbf{\textsf{ Given:-}}}$

• Diagonal of a square is = 10 cm

$\;\;\underline{\textbf{\textsf{ To Find:-}}}$

• Side and perimeter of the square

$\;\;\underline{\textbf{\textsf{ Solution :-}}}$

Let's consider that the given square be ABCD.

In ΔABD :-

Using Pythagoras theorem :-

$\dashrightarrow \sf \: \: {AB}^{2} + {AD}^{2} = {BD}^{2}$

$\dashrightarrow \sf \: \: {a}^{2} + {a}^{2} = {10}^{2}$

$\dashrightarrow \sf \: \: {2a}^{2} = 100$

$\dashrightarrow \sf \: \: {a}^{2} = \dfrac{100}{2}$

$\dashrightarrow \sf \: \: {a}^{2} = 50$

$\dashrightarrow \sf \: \: a = \sqrt{50 }$

$\dashrightarrow \sf \: \: \boxed{ \purple{ \sf{a </p><p>= 5 \sqrt{2} \: cm }}}$

ㅤ$\;\;\underline{\textbf{\textsf{ Hence-}}}$

• Side of the square is 5√2 cm .

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Again, we are asked to find perimeter of the square.

We know that,

$\star\;{\boxed{\sf{\purple{Perimeter _{\;(Square )} = 4 × side)}}}}$

$\dashrightarrow \sf \: \: Perimeter = 4 \times a$

$\dashrightarrow \sf \: \: Perimeter = 4 \times 5 \sqrt{2}$

$\dashrightarrow \sf \: \: \boxed{ \sf{ \purple{ Perimeter = 20 \sqrt{2} \: cm}}}$

ㅤ$\;\;\underline{\textbf{\textsf{ Hence-}}}$

$\underline{\textsf{ Perimeter of the square will be \textbf{ 20√2cm }}}.$

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