A rectangle has a perimeter of 18 inches. a new rectangle is formed by doubling the with W in tripling the length L as shown the new rectangle has a perimeter P of 46 inches a)write and solve a system of linear equation to find the length and width of the original rectangle
b)find the length and width of the new rectangle

a) The dimensions of original rectangle are length= 5 and width= 4.

b) The dimensions of new rectangle are length= 15 and width=8.

Step-by-step explanation:

Original rectangle :

18 = 2(l+w)

18 = 2l + 2w ---------(1)

New rectangle :

46 = 2(3l+2w)

46 = 6l + 4w ---------(2)

Solving the equations :

Multiply (1) by 2 and subtract (2) from (1)

 4l + 4w = 36

-(6l + 4w = 46)

 -2l        = -10

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.