ANSWER :
Base : 15 inches
Height : 4 inches
EXPLANATION :
Recall the area formula of a triangle :
[tex]A=\frac{1}{2}bh[/tex]
The area of the triangle is 30 in^2
The base is 3 inches more than 3 times the height so :
[tex]b=3h+3[/tex]
Using the formula above :
[tex]\begin{gathered} A=\frac{1}{2}bh \\ 30=\frac{1}{2}(3h+3)(h) \\ 60=3h^2+3h \\ 0=3h^2+3h-60 \\ 3h^2+3h-60=0 \\ \text{ Divide both sides by 3 :} \\ h^2+h-20=0 \\ \text{ Factor completely :} \\ (h+5)(h-4)=0 \end{gathered}[/tex]
Equate the factors to 0.
h + 5 = 0
h = -5
h - 4 = 0
h = 4
Since there's no negative dimension, we will only consider h = 4
Solve for the base :
[tex]\begin{gathered} b=3h+3 \\ b=3(4)+3 \\ b=15 \end{gathered}[/tex]
