Diagonal and area are same!

Geometry Level 2

If the area of the square and its diagonal are equal,the what's its side length (find it to 3 decimal places)


The answer is 1.4142.

Rifath Rahman by Rifath Rahman , 19, Bangladesh

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2 solutions

Rifath Rahman
Aug 17, 2014

Let side lengths be x, as area=diagonal or x^2=sqrt 2 or x=sqrt 2=1.4142

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let x x be the side length of the square, then

A = x 2 A=x^2 and d = x 2 + x 2 = x 2 d=\sqrt{x^2+x^2}=x\sqrt{2}

A = d A=d

x 2 = x 2 x^2=x\sqrt{2}

x = 2 x=\sqrt{2}

x = 1.414 \color{#D61F06}\boxed{x=1.414}

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