Pythagoras Theorem. Best Answer 10 Points with workings?

Question

1) Given a triangle, 2 of the sides are given, the opposite and the adjacent, find the hypothenuse.
Adjacent = 2p(p+1), Opposite = 2p+1

Answer 1

From the Pythagoren theorem

(opposite side)^2+(adjacent side)^2 = (hypothenuse)^2

Formula(a=b)^2 = a^2+2ab+b^2

(2p+1)^2+(2p(p+1))^2 = hypothenuse^2

4p^2+1+4p+(2p^2+2p)^2= hypothenuse^2

4p^2+4p+1+4p^4+4p^2+8p^3 = hypothenuse^2

4p^4+8p^3+8p^2+4p+1  = hypothenuse^2

hypothenuse = sqrt (4p^4+8p^3+8p^2+4p+1)