The base of a triangle is 3 cm greaterthan the height.The area is 14 cm^2. Find the height and the leghtof the base.
The height of the triangle is ___cm
The base of the triangle is ___cm
+33665 Area = (1/2)*base*height
14 = (1/2)*(h + 3)*h where h is the height
Multiply both sides by 2 and expand the bracketed term
28 = h^2 + 3h
Subtract 28 from both sides
h^2 + 3h - 28 = 0
This factors as (h + 7)(h - 4) = 0
So the height is either -7 or +4. Since you don't want a negative height then height = 4 cm (so base = 4+3 = 7 cm.
