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the diagonals of a square measure 20. what is the length of a side of the squareleave anwer in simplest radical form

1 Answer

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The square is formed by 2 right triangles, where 20 is the hypotenuse.

We can apply the Pythagorean theorem:

c^2 = a^2 + b^2

Where:

c = hypotenuse = 20

a & b = the other 2 legs of the triangle = s

Since a square has 4 equal sides s, both legs of the triangle are the same (s)

Replacing:

20^2 = s^2+s^2

Solve for s

20^2 = 2 s^2

20^2 = 2 s^2

400 = 2 s^2

400/2 = s^2

200 = s^2

√200 = s

√(2 x 100 ) = s

√2 √100 = s

10 √2 = s

the diagonals of a square measure 20. what is the length of a side of the squareleave-example-1
User Dmitry Sobolevsky
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