Question 459788
Let the base of the triangle = x cm, then the height will be 24-x cm. Since the 

area is {{{54cm^2}}}, we write the equation:

{{{54=x(24-x)/2}}}. Now we solve the equation:Multiply both sides by 2 and 

get:108=24x-x^2}}}. Set the equation equal to zero:

{{{x^2-24x+108=0}}}, solving this quadratic equation  we get x=6 and x=18.

Answer: The base of the triangle is 6cm and the height is 24-6= 18 cm.