Question

the base of a triangle is 11ft more than the height. if the area is 51ft^2 find the base and the height

Answer 1

So.. notice the picture below

and thus, we also know, that A = 51, thus

$\bf A=\cfrac{1}{2}bh\implies A=\cfrac{(h+11)h}{2}\implies A=\cfrac{h^2+11h}{2}\qquad A=51 \\\\\\ 51=\cfrac{h^2+11h}{2}\implies 102=h^2+11h\implies 0=h^2+11h-102 \\\\\\ 0=(h+17)(h-6)\implies \begin{cases} 0=h+17\implies &-17=h\\ 0=h-6\implies &6=h \end{cases}$

now, the height is just a value, it can't be negative, thus  we can rule out -17, thus h = 6

and surely you'd know what the base is