Respuesta :
The height of a triangle is three more than two times the base, can be translated algebraically as
[tex]h=3+2b[/tex]If the area of the triangle is 45 square feet, then we can have the equation
[tex]\begin{gathered} h=3+2b \\ 2b=h-3 \\ b=\frac{h-3}{2} \\ \; \\ A=\frac{1}{2}bh \\ 45=\frac{1}{2}(\frac{h-3}{2})(h) \\ 45\cdot4=\frac{(h-3)h}{4}\cdot4 \\ 180=(h-3)(h) \\ h^2-3h-180=0 \\ (h-15)(h+12)=0 \\ \; \\ h-15=0 \\ h=15 \\ \; \\ h+12=0 \\ h=-12 \end{gathered}[/tex]Disregarding the negative values for h, we use h = 15. And then use this to solve for the base
[tex]\begin{gathered} h=3+2b \\ 15=3+2b \\ 15-3=2b \\ 2b=12 \\ b=6 \end{gathered}[/tex]The dimensions therefore of the triangle is height of 15 feet, and a base of 6 feet.
