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Sagot :
Answer:
length = 500 ft
width= 200 ft
Explanation:
Let us call w the width and L the length of the yard - then we know that
[tex]\frac{w}{L}=\frac{2}{5}[/tex]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
[tex]2(w+L)=1400[/tex]Hence, we have two equations and two unknowns.
Now for solve for w in the first equation to get
[tex]w=\frac{2}{5}L[/tex]substituting this value of w in the second equation gives
[tex]\begin{gathered} 2(w+L)=1400 \\ 2(\frac{2}{5}L+L)=1400 \end{gathered}[/tex]the left-hand side simplifies to give
[tex]2(\frac{7}{5}L)=1400[/tex]dividing both sides by 2 gives
[tex](\frac{7}{5}L)=\frac{1400}{2}[/tex][tex]\rightarrow(\frac{7}{5}L)=700[/tex]Multiplying both sides by 5/7 gives
[tex]\frac{5}{7}\cdot(\frac{7}{5}L)=700\cdot\frac{5}{7}[/tex][tex]L=700\cdot\frac{5}{7}[/tex][tex]L=\frac{700\cdot5}{7}[/tex][tex]\boxed{L=500}[/tex]Hence, the length of the yard is 500 ft.
With the value of length in hand, we now find the width using
[tex]w=\frac{2}{5}L[/tex]since L = 500, the above equation becomes
[tex]w=\frac{2}{5}\cdot500[/tex][tex]w=\frac{2\cdot500}{5}[/tex][tex]\boxed{w=200}[/tex]The width of the yard is 200 ft.
Hence, to summarize
The yard is 200 ft wide and 500 ft long.
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