a) The dimensions of original rectangle are length= 5 and width= 4.
b) The dimensions of new rectangle are length= 15 and width=8.
<u>Step-by-step explanation</u>:
- length of a rectangle = l
- width of a rectangle = w
- Perimeter of a rectangle = 2(l+w)
<u>Original rectangle</u> :
18 = 2(l+w)
18 = 2l + 2w ---------(1)
<u>New rectangle</u> :
46 = 2(3l+2w)
46 = 6l + 4w ---------(2)
<u>Solving the equations</u> :
Multiply (1) by 2 and subtract (2) from (1)
4l + 4w = 36
-(<u>6l + 4w = 46</u>)
<u>-2l = -10</u>
l = 10/2
length = 5 inches.
Substitute l=5 in (1)
18 = 2(5)+2w
18 = 10+2w
2w = 8
w = 8/2
width = 4 inches.
length of new rectangle = 3(l) = 35 = 15 inches.
width of new rectangle = 2(w) = 24 = 8 inches.