Math, asked by dilipsingh3983, 6 months ago

find the side of a square whos diagonal is of 10 cm

Answers

Answered by Anonymous
9

Answer:

It is given that ABCD is a square.

∴ AB = BC = CD = DA = a (say)

According to Pythagoras theorem, in ∆ABD

AB2+AD2=BD2

⇒a2+a2=102

⇒2a2=100

⇒a2=50

⇒a=50

⇒a=52cm

Hence, the side of the square is 5

2

cm.

Now,

Perimeter of a square =

4×(side)

=

4×a

=

4×52

=

202

cm

Hence, the perimeter of the square is 20

2

cm

Answered by Anonymous
76

Given

  • ABCD is a square
  • Diagonal of a square = 10cm

To find

  • Side of the square (a)

Solution

\sf\pink{⟶} In this question, diagonal of a square is given and we have to find the side.

Since, all the sides of a square is equal.

•°• AB = BD = DC = AC = a

\sf\pink{⟶} Using Pythagoras theorem,

\tt:\implies\: \: \: \: \: \: \: \: {AB^2 + AC^2 = BC^2}

\tt:\implies\: \: \: \: \: \: \: \: {a^2 + a^2 = (10)^2}

\tt:\implies\: \: \: \: \: \: \: \: {2a^2 = 100}

\tt:\implies\: \: \: \: \: \: \: \: {a^2 = \dfrac{100}{2}}

\tt:\implies\: \: \: \: \: \: \: \: {a^2 = 50}

\tt:\implies\: \: \: \: \: \: \: \: {a = \sqrt{50}}

\tt:\implies\: \: \: \: \: \: \: \: {\underline{\boxed{\orange{a = 5\sqrt{2}cm}}}}

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