Answer:
length = 500 ft
width= 200 ft
Step-by-step explanation:
Let us call w the width and L the length of the yard - then we know that

in other words, the length to width ratio is 2 : 5.
Moreover, we also know that the distance around the yard (its perimeter) is 1400 ft - meaning

Hence, we have two equations and two unknowns.
Now for solve for w in the first equation to get

substituting this value of w in the second equation gives

the left-hand side simplifies to give

dividing both sides by 2 gives


Multiplying both sides by 5/7 gives




Hence, the length of the yard is 500 ft.
With the value of length in hand, we now find the width using

since L = 500, the above equation becomes



The width of the yard is 200 ft.
Hence, to summarize
The yard is 200 ft wide and 500 ft long.