Expert: Ahmed Salami - 2/19/2010

Question
The base of a triangle is four more than twice its height.  If the area of the triangle is 43 square centimeters find its base and height.

Answer
Hi Jan,
The area of a triangle with base b and height h is
A = bh/2
If base is four more than twice the height,
b = 2h + 4
A = (2h + 4)h/2
 = (h + 2)h
 = h² + 2h
But area is 43cm²
h² + 2h = 43
h² + 2h - 43 = 0
Using the quadratic formula,
h = -2 ± √[2² - (4)(1)(-43)] / 2
 = -2 ± √[4 - (-172)] / 2
 = -2 ± √[4 + 172] / 2
 = (-2 ± √176) / 2
 = (-2 ± √16.√11) / 2
 = (-2 ± 4√11) / 2
 = -1 ± 2√11
We discard the negative value of h because it is impractical, and so
h = (2√11 - 1)cm
b = 2(2√11 - 1) + 4
 = (4√11 - 2) + 4
 = (4√11 + 2)cm

Regards