Question

The area of a triangle piece of aluminum sheeting is 120 inches^2. The base of the triangle is 4 inches more then twice the height. Find the length of the base and height of aluminum triangle.

Answer 1

Length of the base of aluminum triangle is 24 inch

Height of aluminum triangle is 10 inch

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`

now, we can find area of triangle

`A=(1)/(2)* b* h`

now, we can plug b

`A=(1)/(2)* (4+2h)* h`

now, we are given that area =120inch^2

so, we can set it

`120=(1)/(2)* (4+2h)* h`

now, we can solve for h

`240=h\left(4+2h\right)`

`240=4h+2h^2`

`2h^2+4h-240=0`

we can factor out 2

`2(h^2+2h-120)=0`

`(h^2+2h-120)=0`

now, we can factor it

`(h+12)(h-10)=0`

we can set each terms =0

and then we can solve for h

`(h+12)=0`

`h=-12`

`(h-10)=0`

`h=10`

we know that height can never be negative

so, we will only consider h=10

now, we can find b

`b=4+2* 10`

`b=24`

Length of the base of aluminum triangle is 24 inch

Height of aluminum triangle is 10 inch