Question

PLEASE HELP ! The height of a triangle is 4 feet greater than the base. The area of the triangle is 142.5 square feet. Find the length of the base and the height of the triangle

Answer 1

Base:
`15`, Height:
`19`

Explanation:

Let the base be
`b`. Then the height is
`b+4`.

By the area of a triangle theorem, we have that
`bh/2=b(b+4)/2=142.5`.

Multiplying by
`2` and expanding gives
`b^2+4b=285`, so
`b^2+4b-285=0`. We see that this quadratic factors into
`(b-15)(b+19)=0`. Because the base is a side length and must be positive, we have that the base is
`15`.

The height is then
`15+4=19`.