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

Answer:

Base: $15$, Height: $19$

Step-by-step 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 $15+4=19$.