2. the height of a triangle is 5 m less than its base. the area of the triangle is 42 m2. find the length of the base.
(points : 1)

Let's start with what we know

Area:
where 42 is the area, b = base, and h = height

Height:
Since we know the height is 5 less than the base, we can write that as an equation.


Now let's go and plug  into 


Let's distribute b over (b-5)


Let's move 42 over to the right side to make a quadratic formula



Let's plug that into the quadratic equation, which is:


And we can now plug the pieces in to calculate b





Since we can't have a negative value for b (a base can't be negative meters), let's add:





So the base of the triangle is 12m