Find the length and width

Question

The perimeter  of a college athletic field is 104 meters and the length  is 16 m more than the width find the length and width 

Answer 1

P = 104 (given)   perimeter (P) = 2W + 2L    L=16+W   2L=32 + 2W    P = 2W + 32 + 2W   (substituting for 2L)          

 

P = 4W + 32   (simplifying)

 

104 = 4W + 32    72 = 4W  (subtracting 32 from each side)    W = 18   (dividing by 4)   L = 16 + 18   L= 34

 

check (2x18) + (2x34) = 36 + 68 = 104

Answer 2

L = Length

W = Width

 

Perimeter of a rectangle is is 2L + 2W

Perimeter = 104 so 

2L + 2W = 104

 

Length is 16 more than width, so
L = 16 + W

 

Substituting this into the above equation:

 

2(16 + W) + 2W = 104

32 + 2W + 2W = 104

32 + 4W = 104

4W = 72

W = 18

 

So the width is 18 meters

 

The length is 16 + W, so 16 + 18 = 34 meters

Answer 3

Perimeter is length (L) plus width (W) times 2, or 2L + 2W. Here we have L = W + 16. So, we can create the equation:

2(W + 16) + 2W = 104; 2W + 32 + 2W = 104; 4W = 72; W = 18 meters. Then, 2L + 2(18) = 104; 2L = 68; L = 34.

Check 18 + 18 + 34 + 34 = 104 meters.