Question

the length of a rectangle is fixed at 21cm. what widths will make the perimeter greater than 82 cm

Answer 1

width > 20

Answer 2

Well just set up the equation like this,\[P=2l+2w\]but in our case we just want the perimeter to be bigger that a certain value and we know what the length has to be so we can write\[2(21) + 2w > 82\]from there solving for w shouldn't be too bad.

Answer 3

For this, we set up an inequality, since the value has to be greater than 82. This is no problem, as we just replace the equal sign and continue with the equation algebraically.
P<2L+2w, so
82<2(21)+2w
82<42+2w
now we will isolate the variable by subtracting 42 from each side
20<2w
and dividing by 2
10<w
The width must be greater than 10cm in order to create a perimeter of more than 82cm

Answer 4

@Kuromeru: 82-42=40, not 20