Question

The area of a triangle is 3r^4-2r^3-6r^2-3. If its base is (r-2), find the length of its height.

Answer 1

\[(1/2)bh=(1/2)(r-2)(h)=3r ^{4}-2r^{3}-6r ^{2}-3\]
Divide the area by (r-2) to get (1/2)h:
\[(3r^{4}-2r^{3}-6r^{2}-3)/(r-2)= 3r^{3}+4r^{2}+2r+4+5/(r-2)\]
Since this is (1/2)h we multiply it by 2:
\[2(3r^{3}+4r^{2}+2r+4+5/(r-2))=6r^{3}+8r^{2}+4r+4+10/(r-2)\]