Find all possible whole-number lengths and widths of rectangles with each area given below.
a) 12 cm^2
b) 17 cm^2
c) 20 cm^2
d) 24 cm^2
a) 1 * 12, 2 * 6, 3 * 4
b) 1 * 17
I'll be glad to check your answers for c and d.
To find all possible whole-number lengths and widths of rectangles with a given area, we need to find all the factors of the given area.
a) For an area of 12 cm², we can list out the factors: 1 x 12, 2 x 6, and 3 x 4.
The possible dimensions could be length x width: 1 cm x 12 cm, 2 cm x 6 cm, and 3 cm x 4 cm.
b) For an area of 17 cm², the factors are 1 x 17.
In this case, there is only one whole number pair: 1 cm x 17 cm.
c) For an area of 20 cm², we have the factors: 1 x 20, 2 x 10, and 4 x 5.
The possible dimensions are: 1 cm x 20 cm, 2 cm x 10 cm, and 4 cm x 5 cm.
d) For an area of 24 cm², the factors are 1 x 24, 2 x 12, 3 x 8, and 4 x 6.
The possible dimensions could be: 1 cm x 24 cm, 2 cm x 12 cm, 3 cm x 8 cm, and 4 cm x 6 cm.
In summary:
a) Possible dimensions: 1 cm x 12 cm, 2 cm x 6 cm, and 3 cm x 4 cm.
b) Possible dimensions: 1 cm x 17 cm.
c) Possible dimensions: 1 cm x 20 cm, 2 cm x 10 cm, and 4 cm x 5 cm.
d) Possible dimensions: 1 cm x 24 cm, 2 cm x 12 cm, 3 cm x 8 cm, and 4 cm x 6 cm.
By finding the factors of the given areas, we were able to determine all possible whole-number lengths and widths for each rectangle.