# If a=5 and c=13, how do you find b?

##### 1 Answer

Oct 17, 2015

Use Pythagoras and rearrange to find

#### Explanation:

Assuming we're dealing with a right angled triangle with legs of lengths

#a^2+b^2 = c^2#

Subtracting

#b^2 = c^2-a^2#

Then taking the square root of both sides, we get:

#b = sqrt(c^2 - a^2)#

We are told that

#b = sqrt(13^2-5^2) = sqrt(169-25) = sqrt(144) = 12#

**Bonus**

The

#a = 2k + 3#

#b = (a^2 - 1) / 2 = 2k^2+6k+4#

#c = (a^2 + 1) / 2 = 2k^2+6k+5#

This gives us right angled triangles with sides:

#k=0:# #3, 4, 5#

#k=1:# #5, 12, 13#

#k=2:# #7, 24, 25#

#k=3:# #9, 40, 41# ...