Question

the diagonal of a square is 12√2. find its perimeter

Answer 1

dia-12√2
dia-√a×a+a×a
so
12√2-√a×a+a×a
12√2×12√2-a×a+a×a
24×2-4a
48-4a

Answer 2

Answer:

Perimeter of the square (P)= 48 units

Step-by-step explanation:

Let side of a square = a units

Diagonal (d) = 12√2 units /* given

/*We know that,

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

Now ,

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

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

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

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

$\implies a = 12\: units$

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

$\implies P = 48 \: units$

Therefore,

Perimeter of the square (P)= 48 units

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