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If the hypotenuse of a triangle is 30 inches and one of the legs is 10 in, how long is the other leg?

1 Answer

Mar 17, 2018

The leg is #20sqrt2#

Explanation:

We'll solve this using the Pythagorean Theorem.

#a^2 + b^2 = c^2#
where #a# and #b# are the length of the legs , and #c# is the length of the hypotenuse.

Let's plug in the values in the question:
#a^2 + b^2 = c^2#
#10^2 + b^2 = 30^2#
#100 + b^2 =900#
#b^2 = 800#
#b=sqrt800#

Now simplify #sqrt800# to find the exact length:
#sqrt800=sqrt(2×2^2×(2×5)^2)=2×2×5×sqrt2=20sqrt2#

The length of the side is #20sqrt2#

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