Question

The area of a triangle is 16 square units. The base of the triangle is four more than the height of the triangle. What is the base and height of the triangle?

Answer 1

Let x=height. then base is x+4. plug what we know into the formula for the area of a triangle

A=½bh

16=½*(x+4)*(x)

32=x²+4x

x²+4x-32=0
(x+8)(x-4)=0
so x can be-8 our 4. when we plug-8 in for x we get a negative height. since a triangle cannot have a negative side length we discard-8 and try 4. height=4 and base=8