The legs of the isosceles right triangle each measure 14 inches. What is the length of the hypotenuse?

1 Answer
Jackson H.
Sep 12, 2017

#14sqrt2#

Explanation:

First, recognize that an isosceles triangle means two sides are the same. Another keyword here is 'right triangle'. This suggests that it is possible to use the Pythagorean theorem (#a^2 + b^2 = c^2#).

Using this formula, we can easily find the length of the hypotenuse.

In the Pythagorean theorem, #a# and #b# are always the legs of the right triangle, which are the two sides that make up the right angle. The variable #c# is always the hypotenuse. Since we already have both legs, (#14#) all we have to do is substitute.

#14^2 + 14^2 = c^2#
#14^2 = 196#
#196 + 196 = c^2 = 392#
#c = sqrt392#

We can simplify this root by splitting it into its factors.

#392 = 2 * 2 * 2 * 7 * 7#
#sprt392 = sqrt(2 * 2 * 2 * 7 * 7) = sqrt(2*2) * sqrt(2) * sqrt(7*7)#
#=2*7*sqrt2 = 14sqrt2#

Final answer:

#14sqrt2#

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