We're given three overlapping rectangles that create five "sub-rectangles." The yellow sub-rectangle has an area of 96 square centimeters; the light-blue rectangle has an area of 36; the light-green rectangle has an area of 48; the mauve rectangle has an area of 80. The length x is the sum of the "north" side of the yellow rectangle plus the "north" side of the light-blue rectangle. We're given the length of the sum of the "south" sides of the light-green and mauve rectangles: 10 centimeters.
First, note that we can solve for the length of the "west" side of the green rectangle (call it "a") easily enough: we know the area of light-green + mauve = 48 + 80, so we automatically know
10a = 128
Therefore, a = 12.8 cm.
Knowing that, we can solve for the "north" side of the light-green rectangle (b):
12.8b = 48
b = 3.75
This means we can solve for the "east" side of the light-blue rectangle (d, because I chose "c" for the "north" side of the mauve rectangle but never had to use that):
3.75d = 36
d = 9.6
We can now solve for e, the "north" side of the yellow rectangle:
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We're given three overlapping rectangles that create five "sub-rectangles." The yellow sub-rectangle has an area of 96 square centimeters; the light-blue rectangle has an area of 36; the light-green rectangle has an area of 48; the mauve rectangle has an area of 80. The length x is the sum of the "north" side of the yellow rectangle plus the "north" side of the light-blue rectangle. We're given the length of the sum of the "south" sides of the light-green and mauve rectangles: 10 centimeters.
ReplyDeleteFirst, note that we can solve for the length of the "west" side of the green rectangle (call it "a") easily enough: we know the area of light-green + mauve = 48 + 80, so we automatically know
10a = 128
Therefore, a = 12.8 cm.
Knowing that, we can solve for the "north" side of the light-green rectangle (b):
12.8b = 48
b = 3.75
This means we can solve for the "east" side of the light-blue rectangle (d, because I chose "c" for the "north" side of the mauve rectangle but never had to use that):
3.75d = 36
d = 9.6
We can now solve for e, the "north" side of the yellow rectangle:
9.6e = 96
e = 10
The length x is basically the sum of e + b, so
10 + 3.75 = 13.75
x = 13.75
QED.