The length of a rectangle is 9 feet more than the width. If the perimeter is 194 feet, what are the length and the width?

Question

The length of a rectangle is 9 feet more than the width. If the perimeter is 194 feet, what are the length and the width?

Answer 1

Let width of rectangle= w

 

length=l= w+9

 

perimeter=p= 2(l+w) _________ formula of perimeter of rectangle

 

p=194              ______________ given

     

194=2(w+9+w)______________ substitute ( l=w+9)

 

194=2(2w+9) ______________ Combine like terms

 

194=4w+18 _______________ distribution

 

176 =4w _____________ subtract 18 from both sides

 

44 =w _____________ divide by 4 to both sides

 

 

 

 

l=w+9

 =44+9=53

 

so width= 44 feet

     length=53 feet

 

 

Answer 2

The Perimeter (P) of a rectangle = 2 · Length + 2 · Width

 

let x = the width, then x + 9f = length

 

then P = 2(x) + 2(x+9) = 2x + 2x +18 = 4x + 18; given that P = 194f, then 194f = 4x + 18; 176f = 4x; x = 44f

 

thus, the width = 44f and the length = 53f

 

Proof: 2(44f) + 2(53f) = 88f + 106f = 194f

Answer 3

Length = Width + 9

Perimeter = 194 = 2 x Length + 2 x Width

 

Thus: Width = 44 ft and and L = 53