SOLUTION: A rectangle is divided into 4 rectangles with areas, 15 cm2, 45 cm2, 108 cm2 and x cm2. Find the value of x.

Question 761609: A rectangle is divided into 4 rectangles with areas, 15 cm2, 45 cm2, 108 cm2 and x cm2. Find the value of x.
Answer by ramkikk66(644) (Show Source): You can put this solution on YOUR website!
If the rectangle is divided into 4 smaller rectangles, the sums of the lengths of the smaller rectangles would have to add to the larger rectangle and sums of the widths would add to the width of the larger rectangle.
Also, pairs of the smaller rectangles will have the same length, and pairs of them will have the same width.
To find x, we need to know the length and width of the 4th rectangle, which will be the same as the length and width of one of the other 3 rectangles. So let us find out the possible lengths and widths of the other 3 rectangles.
Area = 15: L/W can be: (15,1)(5,3)
Area = 45: L/w can be: (15,3) (9,5) (45,1)
Area = 108: L/w can be: (108,1) (54,2) (36,3) (27,4) (18,6) (12,9)
We can rule out 15 since it does not figure in the 3rd area at all.
Hence the only valid combinations for the 3 rectangles are (5,3), (9,5) and (12,9).
Which means the 4th rectangle has the dimensions (12,3).
Area of the 4th rectangle = 12*3 = 36.
x = 36
You can draw the 4 rectangles and see for yourself :)

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