how many different rectangles are there with an area of 36cm squared if the side lengh of each in centimeters are whole numbers ...please help..me:(
1 + 1 + 17 + 17
2 + 2 + 16 + 16
3 + 3 + 15 + 15
4 + 4 + 14 + 14
5 + 5 + 13 + 13
6 + 6 + 12 + 12
7 + 7 + 11 + 11
8 + 8 + 10 + 10
9 + 9 + 9 + 9
So there are 9.
Indeed there are 9 rectangles with integer side lengths where the perimeter is 36 cm.
For a rectangle with area of 12 cm², you can find the rectangles by identifying all the unique factors of 12.
1*12
2*6
3*4
(4*3 = 3*4)
...
So there are three distinct rectangles with area=12 cm² and with integer sides in cm.
Try the same with area=36.
To find the number of different rectangles with an area of 36cm squared, we need to find all possible pairs of side lengths whose product equals 36. Since the side lengths must be whole numbers, we can start by listing all the factors of 36:
1 x 36 = 36
2 x 18 = 36
3 x 12 = 36
4 x 9 = 36
6 x 6 = 36
From these combinations, we can determine the side lengths of each rectangle. There are five possible combinations:
1) Length = 1cm, Width = 36cm
2) Length = 2cm, Width = 18cm
3) Length = 3cm, Width = 12cm
4) Length = 4cm, Width = 9cm
5) Length = 6cm, Width = 6cm
Thus, there are five different rectangles with an area of 36cm squared, assuming the side lengths are whole numbers.