Question

Can someone help me find the width and the length

Answer 1

Width of the rectangle =
`5k^2`

Length of the rectangle =
`3 k^(2)+7 k+4`

Solution:

Area of the rectangle =
`15 k^(4)+35 k^(3)+20 k^(2)`

Width of the rectangle = greatest common factor of
`15 k^(4), 35 k^(3), \text { and } 20 k^(2)`

Factor of
`15k^4` =
`5*3* k^2 * k^2`

Factor of
`35k^3` =
`5*7* k^2 * k`

Factor of
`20k^2` =
`5*4* k^2`

Greatest common factor of
`15 k^(4), 35 k^(3), \text { and } 20 k^(2)`

=
`5* k^2`

`=5k^2`

Width of the rectangle
`=5k^2`

Area of the rectangle = length × width

`15 k^(4)+35 k^(3)+20 k^(2)=\text{length}* 5k^2`

Divide by 5k² on both sides.

`$(15 k^(4)+35 k^(3)+20 k^(2))/(5k^2) =\frac{\text{length}* 5k^2}{5k^2}`

`$(5k^2(3 k^(2)+7 k+4 ))/(5k^2) =\text{length}`

Cancel the common factor 5k², we get

`3 k^(2)+7 k+4 =\text{length}`

Switch the sides.

Length =
`3 k^(2)+7 k+4`

Width of the rectangle =
`5k^2`

Length of the rectangle =
`3 k^(2)+7 k+4`