Question

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

Answer 1

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

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

Explanation:

• length of a rectangle = l
• width of a rectangle = w
• Perimeter of a rectangle = 2(l+w)

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) = 3
`*`5 = 15 inches.

width of new rectangle = 2(w) = 2
`*`4 = 8 inches.