Suppose two different rt. triangles are there both having natural base natural hypotenuse & natural perpendicular.Their bases are nth powers greater then 2 i.e if one base is a^(n) then the other base is x^(n).Both the bases are joined & their perpendiculars are parallel to each other.Now another rt. triangle is drawn by extending the hypotenuse of the right side triangle & by extending the perpendicular of the left side triangle.
Will we ever get a natural hypotenuse & natural perpendicular for this third triangle?
(Base is natural as it is summation of both the natural bases which are nth powers greater then 2.)
if yes why? if no why?
2006-11-11 01:57:43 · 3 answers · asked by rajesh bhowmick 2 in Science & Mathematics ➔ Mathematics
yes
2006-11-11 19:43:45 · answer #1 · answered by mr. x 5 · 0⤊ 0⤋
yes the new triangle so formed will hv a natural hypotenuse n natural base coz the new perpendicular wiil be 90 degree as it wil form a linear pair wid d earlier perpendicular n d new base will b same so it will b natural 2 n thus it forms a rt triangl
2006-11-11 02:52:20 · answer #2 · answered by mundane gal 2 · 0⤊ 0⤋
yes of course
just multiply each side with (y^n) y aandn integers. and you will get tghe 3rd triangle with integer sides.
2006-11-11 18:32:14 · answer #3 · answered by gjmb1960 7 · 0⤊ 0⤋