In a right triangle, one leg of this triangle represents a distance of (5 SQUARE ROOT 3) miles. the other leg of the triangle is 5 miles shorter then the hypotenuse. What are the lengths of the three sides?

Let be x the hypotenuse
(5√3)^2 + (x5)^2 = x^2
x^2  x^2 10x +25 + 75 = 0
10x = 100
x = 10
(5√3)^2 + (x5)^2 = x^2
x^2  x^2 10x +25 + 75 = 0
10x = 100
x = 10

In this triangle it is given that one side is 5 sqrt 3.let hypotaneous is x then according to question other side will be x5.by pythagoras theorem square of hypotaneous=sq.of base+sq.of perpendicular. x^=(5sqrt3)^+(x5)^ by solving this x=10. hypotaneous is 10 other side is 105 i.e. 5 and the third side is already given.