Answer:
Length of the base of aluminum triangle is 24 inch
Height of aluminum triangle is 10 inch
Step-by-step explanation:
Let's assume height of triangle is h
we are given
The base of the triangle is 4 inches more then twice the height
so, we get length of the base of triangle
![b=4+2h](https://tex.z-dn.net/?f=b%3D4%2B2h)
now, we can find area of triangle
![A=\frac{1}{2}\times b\times h](https://tex.z-dn.net/?f=A%3D%5Cfrac%7B1%7D%7B2%7D%5Ctimes%20b%5Ctimes%20h)
now, we can plug b
![A=\frac{1}{2}\times (4+2h)\times h](https://tex.z-dn.net/?f=A%3D%5Cfrac%7B1%7D%7B2%7D%5Ctimes%20%284%2B2h%29%5Ctimes%20h)
now, we are given that area =120inch^2
so, we can set it
![120=\frac{1}{2}\times (4+2h)\times h](https://tex.z-dn.net/?f=120%3D%5Cfrac%7B1%7D%7B2%7D%5Ctimes%20%284%2B2h%29%5Ctimes%20h)
now, we can solve for h
![240=h\left(4+2h\right)](https://tex.z-dn.net/?f=240%3Dh%5Cleft%284%2B2h%5Cright%29)
![240=4h+2h^2](https://tex.z-dn.net/?f=240%3D4h%2B2h%5E2)
![2h^2+4h-240=0](https://tex.z-dn.net/?f=2h%5E2%2B4h-240%3D0)
we can factor out 2
![2(h^2+2h-120)=0](https://tex.z-dn.net/?f=2%28h%5E2%2B2h-120%29%3D0)
![(h^2+2h-120)=0](https://tex.z-dn.net/?f=%28h%5E2%2B2h-120%29%3D0)
now, we can factor it
![(h+12)(h-10)=0](https://tex.z-dn.net/?f=%28h%2B12%29%28h-10%29%3D0)
we can set each terms =0
and then we can solve for h
![(h+12)=0](https://tex.z-dn.net/?f=%28h%2B12%29%3D0)
![h=-12](https://tex.z-dn.net/?f=h%3D-12)
![(h-10)=0](https://tex.z-dn.net/?f=%28h-10%29%3D0)
![h=10](https://tex.z-dn.net/?f=h%3D10)
we know that height can never be negative
so, we will only consider h=10
now, we can find b
![b=4+2\times 10](https://tex.z-dn.net/?f=b%3D4%2B2%5Ctimes%2010)
![b=24](https://tex.z-dn.net/?f=b%3D24)
Length of the base of aluminum triangle is 24 inch
Height of aluminum triangle is 10 inch