iv) Find the side and perimeter of a square whose diagonal is 10 cm​

1 thought on “iv) Find the side and perimeter of a square whose diagonal is 10 cm​”

1. Given : Diagonal = 10cm

   square is right angled at all vertices so

   we can take any triangle made by the diagonal

   let the two sides be sides AB and AC and let the diagonal be BC ( I am not abusing )

   By using Pythogorus threorem , we can say that

   Since all the sides of a square are equal then we can say that AB = AC

   AB ² + AC ² = BC ²

   AB ² + AB ² = BC ²

   2AB ² = BC ²

   [tex]ab {}^{2} = \frac{10 {}^{2} }{2} [/tex]

   [tex]ab = \sqrt{ \frac{10{}^{2} }{2} } [/tex]

   [tex]ab = \frac{10}{ \sqrt{2} } [/tex]

   So AB = AC

   Therefore each side of this square =

   [tex] sides = \frac{10}{ \sqrt{2} } [/tex]

   Perimeter = 4× side

   [tex]4 \times \frac{10}{ \sqrt{2} } [/tex]

   [tex]perimeter = \frac{40}{ \sqrt{2} } cm[/tex]

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