Answer: (a) 42= 2(3w+3)
(b) L= 2w+3
(c) w=6
l=15
Explanation:
(a): Create an equation in terms of L and W based on the perimeter of the rectangle:
SInce p= 2 (l+w)
All you do is substitute perimeter in (42) for p , 2w+3 for length, and w for width:
42= 2(...+...)
Length is 2w+3 so it'll be:
42=2(2w+3+w)
you can just combine the terms in parenthesis to get
42= 2(3w+3)
(b) Create an equation that relates L and W based on length being 3 feet more than 2x the width:
L= 2w+3 (2 times the width) ( plus 3 more then it)
(c) Solve by find L and W using substitution:
Use your first equation:
42= 2(3w+3)
Solve it:
42= 6w+6
-6 to both to get:
36=6w
Divide by 6
You'll get width= 6
Now using this: L= 2w+3
Plug in 6 for w
L= 2(6)+3
L=15
So,
w=6
l=15
Hope this helps!!!
God bless!!!