Question

The base of a triangle is 3 cm greater than the height. The area is 14cm^2. Find the length and height of the base.

Answer 1

The area of a triangle is
A = base * height /2

If you have not learned to solve quadratic equations before, then think of
2A = base * height
Since A=14, 2A = 28
Look for two integers that multiply together to give 28, but with a difference of 3 between them.

If you have learned quadratic equations, then let
h=height
b=base = h+3

Using the area formula above, you'll get
A=14 = h(h+3)/2
from which you can solve for the height h. The base is simply h+3.

Answer 2

let the height be x cm
then the base is x+3 cm

x(x+3)/2 = 14

solve for x