Answer:
[tex]\large\boxed{A_\triangle==1,536\ in^2}[/tex]
Step-by-step explanation:
The formula of a perimeter of a rectangle:
[tex]P=2(l+w)[/tex]
The formula of an area of a rectangle:
[tex]A=lw[/tex]
l - lenght
w - width
We have l = 3w and the perimeter P = 256 in. Substitute:
[tex]2(3w+w)=256[/tex] divide both sides by 2
[tex]4w=128[/tex] divide both sides by 4
[tex]w=32\ in\to l=3(32)=96\ in[/tex]
Calculate the area of a rectangle:
[tex]A=(96)(32)=3,072\ in^2[/tex]
The triangle ABC is the half of the rectangle. Therefore the area of a triangle ABC is:
[tex]A_\triangle=\dfrac{3,072}{2}=1,536\ in^2[/tex]
