Question

if the diagonal of a square is 288m.then the length of the square?​

Answer 1

$\: \:~~~~~ \: \: \: \:\: \: \: \: \: \: \: \bf \underline{Solution}$

Given

• Diagonal of a square = 288m

To Find

• Side of the square.

★ Solution 1

We know that

${~ \sf~~~~:~~\implies Diagonal ~of ~a~ square= \sqrt{2} ~Side}$

${~ \sf~~~~:~~\implies \sqrt{2} ~Side = 288}$

${~ \sf~~~~:~~\implies ~Side = \dfrac{288}{ \sqrt{2} } }$

${~ \sf~~~~:~~\implies ~Side = \dfrac{288}{ 1.41421356237 . \: . \: . \: . \: } }$

${~ \sf~~~~:~~\implies ~Side ≈ 203.6467. \: . \: . \: . \: }$

Hance,

• The length of Square is 203.6464...

_____________________

★ Solution 2

Let the side of Square be x.

We know that

All angles in a Square is 90°.

therefore, ABC is a Right Angle Triangle.

By Using Pythagoras Theorem

$\sf ~~~~~:~~\implies AC²= AB²+ BC²$

$\sf ~~~~~:~~\implies x² = 82944$

$\sf ~~~~~:~~\implies 2x² = 82944$

$\sf ~~~~~:~~\implies x² = 41472$

$\sf ~~~~~:~~\implies x = \sqrt{ 41472}$

$\sf ~~~~~:~~\implies x ≈ 203.6467. \: . \: . \: . \: . \: . \:$

Hance,

• The length of Square is 203.6464...

Figure of Square:

$\setlength{\unitlength}{2mm}\begin{picture}(10,10)\linethickness{0.5mm}\put(6,2){\dashbox{0.01}(15,15)}\put(3,0){\bf D}\put(3,18){\bf A}\put(23,18){\bf B}\put(23,0){\bf C}\end{picture}$