Asked by Katherine
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:(
Answers
Answered by
Anthony
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.
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.
Answered by
MathMate
Indeed there are 9 rectangles with integer side lengths where the <i>perimeter</i> is 36 cm.
For a rectangle with <i>area</i> 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.
For a rectangle with <i>area</i> 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.
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