Mathematics: The diagonal of a square has a length of eight times begin square root two end square root cm. find the length of a side of the square. a. 8 cm b. 4 cm c. two times begin square root two end square root cm d. five times begin square root two end square root cm

The square root of x^2 / 24 x 6/xTHis is equal to sqr(x -5)...

The diagonal of a square has a length of eight

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17.01.2022

ANSWER

A. 8cm

EXPLANATION

The diagonal of the square is

$d = 8 \sqrt{2} cm$

Let the length of each side of the square be l units.

Then the diagonal and any two sides form an isosceles right triangle with the diagonal being the hypotenuse.

We use the Pythagoras Theorem, to obtain,

${l}^{2} + {l}^{2} = {d}^{2}$

This implies that,

$2 {l}^{2} = (8 \sqrt{2} )^{2}$

$2{l}^{2} = 128$

Solve for l,

${l}^{2} = 64$

Take positive square root of both sides

$l = \sqrt{64}$

l = 8cm

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