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

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

$b=4+2h$

now, we can find area of triangle

$A=\frac{1}{2}\times b\times h$

now, we can plug b

$A=\frac{1}{2}\times (4+2h)\times h$

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

so, we can set it

$120=\frac{1}{2}\times (4+2h)\times h$

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

$b=4+2\times 10$

$b=24$

Length of the base of aluminum triangle is 24 inch

Height  of aluminum triangle is 10 inch