Answer:
l = 60 yd; w = 30 yd
Step-by-step explanation:
We have two bits of information
(a) The perimeter of the rectangle
The formula for the perimeter of a rectangle is
P = 2l + 2w
P = 180 yd Insert into the formula
(1) 2l + 2w = 180
===============
(b) The length-to-width ratio
(2) l = 2w
Substitute the value of l from Equation (2) into Equation (1)
2×(2w) + 2w = 180
===============
Solve for w
4w + 2w = 180 Combine like term
s
6w = 180 Divide each side by 6
w = 30 yd
===============
Solve for l
Substitute the value for w into Equation (1).
2l +2×30 = 180
2l +60 = 180 Subtract 60 from each side
2l = 120 Divide each side by 2
l = 60 yd
The field is 60 yd long and 30 yd wide.
===============
<em>Check</em>:
P = 2×60 + 2×30
P = 120 + 60
P = 180 yd
Also
60 = 2 × 30
60 = 60
