In order to begin we must start off with the formula for the area of a triangle, which is a=1/2b(h) where a is area, b is base, and h is height.
In this scenario, we know that the area is 45cm^2 and the base is 2h+12 (since it is twice it’s height plus twelve). We can plug this into the area equation and then proceed to solve out accordingly. a=1/2b(h) 45=1/2(2h+12)(h) 90=(2h+12)(h) 90=2h^2 + 12h 0= 2h^2 + 12h - 90
Simplify by dividing the two out.
h^2 + 6h - 45 = 0.
Now plug into the quadratic formula (with a=1, b=6, and c=-45) as shown in the image below.
After plugging the equation in and solving, we come to the idea that h is roughly equal to 4.34. We can now plug this back into the triangle area formula to solve out for b. a=1/2b(h) 45=1/2(2h + 12)(h) 45=1/2(20.69)(4.34) 45=45.
In conclusion; The height is ≈ 4.34 The base is ≈ 8.68
