The height of the triangle = 16 yards
The base of the triangle = 21 yards
Explanations:Let the height of the triangle be h
Height = h
The base is 5 yards longer than the height
Base = h + 5
The area = 168 square yards
[tex]\text{The area of a triangle = }\frac{1}{2}\times base\times height[/tex][tex]\begin{gathered} 168\text{ = }\frac{1}{2}\times(h+5)\times h \\ h(h+5)\text{ = 2(168)} \\ h^2+5h\text{ = }336 \\ h^2+5h-336\text{ = 0} \\ \end{gathered}[/tex]Solve the resulting quadratic equation:
[tex]\begin{gathered} h^2-16h+21h-336=0 \\ h(h-16)+21(h-16)=0 \\ (h-16)(h+21)\text{ = 0} \\ h-16=0 \\ h\text{ = 16} \\ h+21=0 \\ h\text{ = -21} \end{gathered}[/tex]The height of the triangle = 16 yards
The base of the triangle = 16 + 5
The base of the triangle = 21 yards
