Given that the perimeter of a rectangle is 44cm, and that the rectangle is divided into 5 congruent rectangls, find the measure of each of the rectangles.
There is not enough information given to give a unique answer. Let the length be given by 5a, so the width is (22-5a). Note that 5a+(22-5a)+5a+(22-5a)=44=the perimeter. Then each of the subdivided rectangles has dimensions l by (22-5a). e.g. for a=1 you have the large rectangle with dimension 5x17, and each small rectangle with dimensions 1x17; if a=2 you have the large rectangle with dimensions 6x16, and each small rectangle with dimensions 6/5x16.
a a a a a total length=5a
| | | | | | width = 22-5a
If you are also given another constraint, for instance the area of either the large rectangle or one of the subdivided rectangles, or are asked to find the largest such rectangle by area, then you could give a unique singular answer.
As the question is stated, let the length be 5a, then the widthis (22-5a) and each of the small rectangles has dimensions ax(22-5a).
*(The area of the large rectangle is 5a*(22-5a) and the area of each small rectangle is a*(22-5a).