Question

The length of a rectangle is 55 times the width. the area is 845845 square yards. find the length and width of the rectangle.

Answer 1

Width = w

Length = 55 times w. Therefore, length = 55w

Area = width ⋅ length

Area = w ⋅ 55w

845,845
`yards^(2)` = 55w ⋅ w

845,845
`yards^(2)` = 55
`w^(2)`

Divide both sides by 55 to get "w" by itself.


`(845,845 yards^(2) )/(55)` =
`( 55w^(2) )/(55)`

15,379
`yards^(2)` =
`w^(2)`

Now, take the square root of *both* sides in order to solve for "w."


`\sqrt{15,379 yards ^(2) } = \sqrt{ w^(2) }`

The square root of 15,379 simplifies to 13
`√(91)`.

Therefore, width equals 13
`√(91)` and length equals 55 times that.

Length equals 715
`√(91)`.

Practically, you'll want to round those values (to the nearest hundredth is sufficient).

For a rectangle that is 845,845
`yards^(2)`, the width is roughly 124.01 yards and the length is 6820.67 yards.