SOLUTION: one side of the triangle is 10 the other is 5 and the last is unknown using c squared=a squared + b squared what is the working out and the last side

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Question 1098036: one side of the triangle is 10 the other is 5 and the last is unknown
using c squared=a squared + b squared what is the working out and the last side

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!

You didn't say the triangle was a right triangle. However, since you are using a%5E2%2Bb%5E2=c%5E2 I will assume it is.

There are of course two possibilities, with two different answers. The missing side could be the longest side (hypotenuse), with the 5 and 10 being the legs; or the 10 could be the hypotenuse, with the missing side one of the legs.

(1) If the hypotenuse is the missing side, then it is c, and the 5 and 10 are the a and b. So
5%5E2%2B10%5E2+=+c%5E2
25%2B100+=+c%5E2
125+=+c%5E2
c+=+sqrt%28125%29+=+5%2Asqrt%285%29

(2) If 10 is the hypotenuse, then
5%5E2%2Bb%5E2+=+10%5E2
25%2Bb%5E2+=+100
b%5E2+=+75
b+=+sqrt%2875%29+=+5%2Asqrt%283%29