Question 841584: A large rectangle has been subdivided into four non-overlapping smaller rectangles by two lines, one parallel to the base of the large rectangle and the other parallel to its height. The base and height dimensions of all five of the rectangles are all integer values. Hence, the areas of all five of the rectangles also have integer values. The areas of three of the smaller rectangles are 18, 24, and 40 square units.
Your tasks are to determine:
a) the area of the fourth smaller rectangle,
b) the area of the large rectangle, and
c) the base and height dimensions of all five of the rectangles.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! I'm not sure how you're supposed to get this, but the answer that I got was that the area of the fourth rectangle is equal to 30.
If you draw a rectangle and then divide it into 4 separate rectangles, then you will have 3 of the smaller rectangles with known area and you will need to find the area of the fourth.
I put the rectangle with 18 square units on top left and the r4ectangle with 24 square units on bottom left.
these rectangles could have different heights but had to have the same width.
alternately they could have had different widths but had to have the same height.
i chose the former.
since 6 divided evenly into 18 and 24, i chose a width of 6 for both rectangles.
this gave the top left rectangle a height of 3 and the bottom left rectangle a height of 4.
this means that the top right and bottom right rectangles had to have a height of 3 and 4 respectively.
since 40 is divisible by 4, i chose the bottom left rectangle to have a height of 4 and a width of 10.
this forced the top right rectangle to have a width of 10 since both rectangles on the right half had to have the same width.
that gave the top right rectangle an area of 30.
the total area was 18 + 24 + 30 + 40 = 112 square unis.
the total dimensions were length of 7 and width of 16.
take 6 * 16 and you get an area of 112.
numbers checked out so the solution is good.
the rectangle would look like this:
6 10
3 18 30 3
4 24 40 4
6 10
The 6 and 10 on the top and bottom horizontal display are the widths of each of the smaller rectangles.
The 3 and 4 on the left and right vertical display are the lengths of each of the smaller rectangles.
their areas are in the middle.
the top left rectangle is 3 by 6.
the top right rectangle is 3 by 10.
the bottom left rectangle is 4 by 6.
the bottom right rectangle is 4 by 10.
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