Question

The height of a triangle is 4 m more than twice the length of the base. The area of the triangle is 63 m2. Find the height of the triangle.

Answer 1

If length b, h=4+2b, A=1/2bh = 63
\[^{1}_{2}bh=63\]
\[^{1}_{2}\times b \times(4+2b)=63\]
\[b \times (4+2b)=126\]
\[4b+2b ^{2}=126\]
Divide both sides by 2
\[b ^{2}+2b=63\]
\[b ^{2}+2b -63=0\]
Plug into the quadratic equation and solve for b
b=-9, b=7

Check: 1/2 7*(4+2*7)=63
1/2*7(4+14)=63
1/2*126=63
63=63