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Byju's Answer
Standard VII
Mathematics
Perimeter of a Square
If the diagon...
Question

If the diagonal of a square is 12√2 cm, then the perimeter of square is ____

A
24 cm
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B
24√2 cm
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C
48 cm
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D
48√2 cm
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Solution

The correct option is B 48 cm

Perimeter of the square (P)= 48 units

Step-by-step explanation:

Let side ofasquare=aunits

Diagonal(d)=12√2units/*given

Now ,

\boxed {Area \: of \the \: square (A)\\=a^{2}=\frac{d^{2}}{2}}

a^{2} = \frac{(12\sqrt{2})^{2}}{2}

\implies a^{2}=\frac{12^{2}\times 2}{2}

\implies a^2 = (12\:unit)^{2}

\implies a = \sqrt{12^{2}}

\implies a = 12\: units

Perimeter \: of \: the \: square (P) = 4r\\=4 \times 12 \:units

\implies P = 48 \: units

Therefore,

Perimeterofthesquare(P)=48units


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