The legs of a right triangle have the proportion 8:15, and the hypotenuse is 6.8 cm long. Find the area of the triangle.

Solution:Let the legs be 8x and 15x.The hypotenuse is 6.8 cm long.Using Pythagoras theorem we can write [tex](8x)^2+(15x)^2=(6.8)^2\\ \\ 64x^2+225x^2=(6.8)^2\\ \\ 289x^2=(6.8)^2\\ \\ 17x=6.8\\ \\ x=0.4\\[/tex]So the legs are [tex]8x=8*0.4=3.2\\ \\ 15x=15*0.4=6\\[/tex]Are of Triangle[tex]=\frac{1}{2}base*height\\[/tex]Are of Triangle[tex]=\frac{1}{2}3.2*6=9.6cm^2\\[/tex]