Question

the diagonal of a square is 72 cm find the side of the square​

Answer 1

Question :---- the diagonal of a square is 72 cm find the side of the square ?

Formula used :---

→ Each side of Square are of similar side, and each angle is 90° .

→ Pythagoras Theoram = Base² + Perpendicular ² = Hypotenuse² .

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Solution (1) :----

Lets Solve it with basic Method First .

Let Each side of Square is = a cm.

Now,

When we construct a diagonal with Two vertices , [ Refer To image once].

In ∆ABC ( From image ) we have,

→ Angle BAC = 90°

→ side AB = AC = side of square = a cm.

→ BC = Diagonal = d.

Now, using pythagoras in Right ∆ ABC, we get,

→ a² + a² = d²

→ 2a² = d² ------------------- Equation (1)

Putting value of d = 72 now, we get,

→ 2a² = (72)²

Dividing both sides by 2 we get,

→ a² = 72*36

→ a² = 2*36*36

→ a² = 2*(6*6)*(6*6)

Square root both sides now,

→ a = 6*6√2

→ a = 36√2 cm.

Hence, side of Square will be 36√2 cm..

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Solution (2) :-----

From Equation (1) now, we can also say that,

→ Diagonal of a square is Equal to = √2a . { when we Square root both sides of Equation one we get this Formula. we can directly remember this . or we can prove like i told you by pythagoras theoram }...

So,

→ D = √2a

Putting value of D ,

→ 72 = √2a

Dividing both sides by √2 now,

→ a = 72/√2

Rationalizing the RHS part now,

→ a = (72/√2) * (√2/√2)

→ a = (72√2)/2

→ a = 36√2.

So, Side of Square will be 36√2cm.

Answer 2

$\huge\mathbb{SOLUTION:-}$

Given

the diagonal of square is 72cm

• we have to find the side of square

Now

$\bf\underline{\underline{According \:To\: Question:-}}$

• By Pythagoras formula we can find our answer

$\boxed{\sf{Diagonal{}^{2}=base{}^{2}+perpendicular {}^{2}}}$

• We know that all sides of square are equal

• Let the side of square be x

$\sf\implies (72){}^{2}=x{}^{2}+x{}^{2}\\ \\ \sf\implies 72\times 72=2x{}^{2}\\ \\ \sf\implies \cancel{\dfrac{\cancel{72}\times 72}{2}}=x{}^{2}\\ \\ \sf\implies 36\times 72=x{}^{2}\\ \\ \sf\implies x=\sqrt{36\times 72}\\ \\ \sf\implies x= \sqrt{36\times 36\times 2}\\ \\ \sf\implies x=36\sqrt{2}$

• The side of square is 36√2

Lets verify :-

$\boxed{\bf{VERIFICATION:-}}$

$\sf\implies x{}^{2}+x{}^{2}=d{}^{2}\\ \\ \sf\implies 2x{}^{2}=d{}^{2}\\ \\ \sf\implies x=\:\:(36\sqrt{2})\\ \\ \sf\implies 2\times (36\sqrt{2}){}^{2}=(72){}^{2}\\ \\ \sf\implies 2\times 1296\times 2=5184\\ \\ \sf\implies 5184=5184\\ \\ \sf\:\:\:L.H.S=R.H.S\:\:$

$\boxed{\sf{Side\:of\:square=36\sqrt{2}}}$