The area of a triangle is 24 square meters. the base is 2 meters more than the height. what are the base, b, and the height, h, of the triangle

A of Δ =

let h = x
thus b = x + 2

If A = 24 
  by substituting b, h and A into equation

⇒  

⇒  

⇒  

⇒ x² + 8x - 6x - 48 = 0

⇒ (x + 8) (x - 6) = 0

   thus x = -8  OR  x = 6 

∴ height = 6 m; base = 8 m  ( x = -8  was disregarded since a                                                                       measurement of this kind cannot be negative)