Question

A right triangle has hypotaneous of length q cm and one side of length p cm .If (q-p)=2,express the length of third side of the triangle in terms of q.

Answer 1

since (q-p)=2

therefore , p=q-2

now , let the third side be = r

Now by pythagoras theorm,

p²+r² = q²

r² = q²-p²

r² = q²-(q-2)²

r² = q²-(q²+4-4q)

r² = q²-q²-4+4q

r² = 4q-4

r² = 4(q-1)

r = √4(q-1)

Therefore, r = 2√q-1

Hence the third side in terms of q will be equal to 2√q-1