How do you find the length of the missing side given a? b=24 c=40?

1 Answer
Jun 29, 2016

Answer:

a = 32

Explanation:

To answer this problem, you should use the Pythagorean Theorem:

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The hypotenuse (c=40) and one of the legs (b=24) are known, so all we have to do is solve for a. We can do that by plugging in our known values:

#a^2+24^2=40^2#

#24^2# or #24xx24# = 576
#40^2# or #40xx40# = 1600

Thus, #a^2+576=1600#. Now subtract 576 from both sides of the equation to get #a^2# by itself:

#a^2+576=1600#
-576 -576

You should end up with:

#a^2=1024#

Next, take the square root of both sides to find a. The square root
(#sqrt#) is the inverse of the square (#a^2#)

#sqrt (a^2) = sqrt1024#

Therefore, a = 32

You can check your answer by plugging a and b into the equation and solve for c to see if your answer matches the given value of c:

#32^2+24^2=40^2#