Width = w
Length = 55 times w. Therefore, length = 55w
Area = width ⋅ length
Area = w ⋅ 55w
845,845[tex]yards^{2} [/tex] = 55w ⋅ w
845,845[tex]yards^{2} [/tex] = 55[tex] w^{2} [/tex]
Divide both sides by 55 to get "w" by itself.
[tex] \frac{845,845 yards^{2} }{55} [/tex] = [tex] \frac{ 55w^{2} }{55} [/tex]
15,379 [tex] yards^{2} [/tex] = [tex] w^{2} [/tex]
Now, take the square root of *both* sides in order to solve for "w."
[tex] \sqrt{15,379 yards ^{2} } = \sqrt{ w^{2} }[/tex]
The square root of 15,379 simplifies to 13[tex] \sqrt{91} [/tex].
Therefore, width equals 13[tex] \sqrt{91} [/tex] and length equals 55 times that.
Length equals 715[tex] \sqrt{91} [/tex].
Practically, you'll want to round those values (to the nearest hundredth is sufficient).
For a rectangle that is 845,845 [tex]yards^{2} [/tex], the width is roughly 124.01 yards and the length is 6820.67 yards.
