Answer:
Explanation:
The height of the triangle is
[tex]2x+2+x+6=3x+8[/tex]
the base length is
[tex]2(3x+5+3)=6x+16[/tex]
Therefore, the area of the larger triangle is
[tex]Area=(6x+16)(3x+8)[/tex]
Similarly, the area of the shaded triangle is
[tex](x+6)(3x+5)[/tex]
Therefore, the area of the unshaded region is
[tex](6x+16)(3x+8)-(x+6)(3x+5)[/tex]
which simplifies to give
[tex]15x^2+73x+98[/tex]
and we know that the area of the unshaded region is 315 and so
[tex]15x^2+73x+98=315[/tex]
which simplifies to give
[tex]15x^2+73x-217=0[/tex]
and the solution to the equation is
[tex]x=2.082[/tex]
With the value of x in hand, we now find the base and height lengths.
[tex]\begin{gathered} height=3x+8=3(2.082)+8 \\ \boxed{height=14.246} \end{gathered}[/tex]
and
[tex]\begin{gathered} base=6x+16=2(2.082)+16 \\ \boxed{base=20.164} \end{gathered}[/tex]
Hence,
height = 14. 246
base = 20.164
