Question 916621
Let B represent the base of the billboard and H represent its' height. From the problem we know that {{{B = H + 10}}}

Then using common knowledge, we know that standard billboards are rectangular in shape. Therefore, the relationship of B and H to the Area, represented by A is: {{{A = BH = 336 }}}

We have 2 equations, and 2 unknowns. We can plug the height equation into our area equation to get: {{{336 = H(H+10)}}} or {{{336 = H^2 + 10H}}} This is a simple quadratic equation, therefore we can use the quadratic formula {{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a)}}} to find B, where a = 1, b = 10, c = -336.

The solutions to this are 14 and -24. Since we know these types of quantities cannot be negative, we take the positive root, 14, meaning the base is 24 ft and the height is 14 ft. To check this we simply compute 24*14 and we find it does indeed equal 336, the area of the advertising space.