Question

The perimeter of rectangle ABCD is 256 inches. Its length is 3 times as long as its width. Find the area of triangle ABC.

Answer 1

Answer:

$\large\boxed{A_\triangle==1,536\ in^2}$

Step-by-step explanation:

The formula of a perimeter of a rectangle:

$P=2(l+w)$

The formula of an area of a rectangle:

$A=lw$

l - lenght

w - width

We have l = 3w and the perimeter P = 256 in. Substitute:

$2(3w+w)=256$               divide both sides by 2

$4w=128$               divide both sides by 4

$w=32\ in\to l=3(32)=96\ in$

Calculate the area of a rectangle:

$A=(96)(32)=3,072\ in^2$

The triangle ABC is the half of the rectangle. Therefore the area of a triangle ABC is:

$A_\triangle=\dfrac{3,072}{2}=1,536\ in^2$