Question

On a centimeter dot grid, draw all possible rectangles with a perimeter of 16 cm and sides whose lengths are whole centimeter. Label the lengths of two adjacent sides of each rectangle.

Answer 1

See attachment

Explanation:

The perimeter of a rectangle is the sum of the lengths of all the sides of the rectangle, so it is given by:

`p=2L+2w`

where

L is the length

w is the width

In this problem, we want to find all the integer values of L and w such that the perimeter is 16 cm:

`p=16 cm`

This means:

`16=2L+2w`

Or:

`16=2(L+w)\\\rightarrow L+w=8`

We have only 4 possible combinations:

L = 7 cm, w = 1 cm

L = 6 cm, w = 2 cm

L = 5 cm, w = 3 cm

L = 4 cm, w = 4 cm

The other combinations with L and w swapped are identical, so we don't include them; therefore, these are the only 4 possible combinations. The 4 possible rectangles are therefore draw in attachment.