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

Jun 29, 2016

a = 32

#### Explanation:

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

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 $24 \times 24$ = 576
${40}^{2}$ or $40 \times 40$ = 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 (${a}^{2}$)

$\sqrt{{a}^{2}} = \sqrt{1024}$

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:

${32}^{2} + {24}^{2} = {40}^{2}$