Find the area of the rectangle if the length is three times the width and the perimeter is 16.

Let the length of the rectangle be L and the width be
w.

Given that the length of the rectangle is 3 times the
width.

Then we will write:

L =
3*w ..............(1).

Also, given that the perimeter of
the rectangle is 16.

Then we will
write:

==> 2L + 2W =
16

We will divide by
2.

==> L + w =
8...........(2)

Now we will substitute with L =
3w

==> 3w + w =
8

==> 4w = 8

==>
w= 2

==> L = 3*2 =
6

Then, the length of the rectangle is 6, and the width is
2 .

Now we will calculate the area of the
rectangle.

We know that the area of the rectangle is given
by:

A = L * w

==> A =
2*6 = 12

Then, the area is 12 square
units.