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Murljashka [212]
3 years ago
12

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
Mathematics
1 answer:
vladimir1956 [14]3 years ago
8 0

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) = 3\times5 = 15 inches.

width of new rectangle = 2(w) = 2\times4 = 8 inches.

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