Answer:
the height is 5 and the base is 17.
Step-by-step explanation:
X + 1 is the height and 4x + 1 is the base, so we can substitute this into an equation:
( x + 1 ) (4x + 1) = 85
{apply the distributive law}
4x² + x + 4x + 1 =
4x² + 5x + 1 = 85
Take 85 to the other side by -85 each side:
4x² + 5x + 1 - 85 = 85 - 85
4x² + 5x - 84 = 0
{Now we have a quadratic equation}
The roots are either -5.25 or 4. X must be 4 since it must be positive as it is a side length.
Substitute x into the base and height to get the answers.
X + 1 = 4 + 1 = 5
4x + 1 = 16 + 1 = 17
Therefore the height is 5 and the base is 17.
