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# Advanced Use Of The Pythagorean Theorem? (square roots)

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If the Hypotenuse of a 45-45-90 triangle is $$3\sqrt{2}$$, what are the lengths of the other 2 sides? Please explain.

#3
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In a 45-45-90  right triangle, the legs are  1/sqrt(2)  as long as the hypotenuse....

So.....the legs are  3sqrt(2) * (1 / sqrt(2))   =    3  units long

CPhill  Feb 8, 2016
#1
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I got 2.9999999... Please tell me if this is correct.

#2
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Both legs are equal to 3 because they are congruent and equal 3*(sqrt(2))/sqrt(2).

Reason: 45-45-90 Thrm.

Both legs are congruent, hypotenuse is leg*sqrt(2)

rarinstraw1195  Feb 8, 2016
edited by rarinstraw1195  Feb 8, 2016
#3
+88775
+10

In a 45-45-90  right triangle, the legs are  1/sqrt(2)  as long as the hypotenuse....

So.....the legs are  3sqrt(2) * (1 / sqrt(2))   =    3  units long

CPhill  Feb 8, 2016
#4
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If the Hypotenuse of a 45-45-90 triangle is 3root2 , what are the lengths of the other 2 sides? Please explain.

This is a standard 45-45-90 triangle.

The sides must stay in the same proportion.

If you multiply the hypotenuse by 3 you can see it will be    $$3\sqrt2\;\;\;units$$

So you must multiply the other sides by 3 as well.   1*3=3

SO

the other sides will be 3

Melody  Feb 9, 2016