The width of a rectangle is fixed at 28 cm. What lengths will make the perimeter greater than 72 cm?

1 Answer
Stefan V.
Oct 16, 2015

#l > "8 cm"#

Explanation:

Start by writing down the formula for the perimeter of a rectangle

http://calculus-geometry.hubpages.com/hub/How-to-Find-the-Area-Perimeter-and-Diagonal-of-a-Rectangle

#"perimeter" = P = 2 xx (l + w)" "#, where

#l# - the length of the rectangle;
#w# - its width.

In your case, you know that the width of the rectangle is set at #"28 cm"#. In order to find which lengths would make the perimeter greater than #"72 cm"#, determine what exact length will make the perimeter exactly #"72 cm"#.

#P = 2 xx (l + 28) = 72#

#l + 28 = 72/2#

#l = 36 - 28 = "8 cm"#

This means that for any length that exceeds #"8 cm"#, the perimeter of the rectangle will be greater than #"72 cm"#.

#2 x (l + 28) > 72#

#l + 28 > 36#

#l > "8 cm"#

SIDE NOTE Don't be confused by the fact that the length turned out to be "shorter" than the width, that happens in some cases.

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