A right triangle has legs of length 10 and b, and a hypotenuse of length c. The perimeter of the triangle is 30. Compute c.

Perimeter =10 + b + c

30 =10 + b + c

20 = b + c

c = 20 - b.......................(1)

By Pythagoras's Theorem:

c^2 =10^2 + b^2.........(2)         sub c from (1) above into (2)

(20 - b)^2 = 10^2 + b^2

400 -40b + b^2 =100 + b^2    subtract 100 + b^2 from both sides

300 - 40b =0                               add 40b to both sides

300 =40b                                     divide both sides by 40

b =300 / 40

b=7.5                                         sub this into (1) above

c =20 - 7.5

c = 12.5 - This is accurate, because:

12.5^2 =7.5^2 + 10^2

156.25 =56.25 + 100