The longer leg of a right triangle is three times as long as the shorter leg. The hypotenuse is $\sqrt 5.$ What is the area of this triangle?

Answer 1

x^2 + (3x)^2 = 5

10x^2 = 5

x^2 = 1/2

x = sqrt(2)/2

the legs are sqrt(2)/2 and 3*sqrt(2)/2

the area is (1/2)(sqrt(2))(2*sqrt(2)/2) = 1