Answer 1..........:Length: 9 inches
Width: 3 inches
Explanation:
You use the information given to you to write a system of two equations.
The perimeter of a rectangle is equal to the sum of its length and its width, multiplied by
2
P
=
2
⋅
(
L
+
w
)
In your case, you know that
2
(
L
+
w
)
=
24
This will be your first equation.
Now focus on the fact that its length is 3 times greater than its width. This can be written like this
L
=
3
⋅
w
Your system will be
{
2
(
L
+
w
)
=
24
L
=
3
w
To solve for the length and width of the rectangle, use the expression you have for
L
in the first equation to get
w
2
⋅
(
3
w
+
w
)
=
24
2
⋅
4
w
=
24
⇒
w
=
24
8
=
3
This means that
L
is equal to
L
=
3
⋅
3
=
9
Step-by-step explanation: 2........
