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# Pythagorean theorem

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a community is building a square park with sides that measure 120 meaters. to seperate the picnic area from the play area, the park is split by a diagonal line from opposite corners. determine the approximate length of the diagonal line that splits the square. if necessary, round your answer to the nearest tenth.

Guest Apr 29, 2017
#1
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The two sides of the triangle are 120 "meaters" long.

Pythagorean theorem is as follows:

$$c^2=a^2+b^2$$

"a" and "b" are the sides. "c" is the diagonal.

So substitute the length in:

$$c^2=120^2+120^2$$

And simplify

$$14400+14400=c^2$$

$$28800=c^2$$

$$c=\sqrt{2880}$$

$$c=24\sqrt{5}≈53.7$$

$$24\sqrt{5}$$    or    $$53.7$$

Guest Apr 29, 2017
#2
+7324
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Ah something is slightly off..the diagonal must be longer than the length of the sides...!

I think you forgot a one zero at the end...it should be

$$c=\sqrt{28800}=120\sqrt2 \approx 169.706$$      (meters)

hectictar  Apr 30, 2017