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

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

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=(3,072)/(2)=1,536\ in^2`