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Sunday, July 16, 2023
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We're given 4 boxes—blue, yellow, green, and mauve(?). Yellow and green are stacked perfectly atop each other. Blue is to the left of yellow and the same height; mauve is to the right of green and the same height. The area of yellow is 28 sq. cm; the area of mauve is 14 sq. cm. The long length of blue + yellow is 9 cm; the long length of green + mauve is 10 cm; the height of mauve and green is 5 cm. That's all we know, and we have to solve for the area of blue.
ReplyDeleteSince we know the height and area of mauve, let's start there.
5x = 14
x = 14/5
The short side of mauve is 14/5, and the total length of the long side of green + mauve is equal to 10, so the long side of green is:
10 - (14/5) = 36/5
To find the height of yellow, then, we go
(36/5)x = 28
x = 35/9
That's the height of the blue rectangle as well.
The long length of blue + yellow is 9, and we know the long length of just yellow is 36/5, so to find the short length of blue, we go
x + 36/5 = 9
x = 9/5
We now know the two dimensions we need to calculate the area of blue.
(35/9)•(9/5) = 35/5 = 7.
The area of blue is 7 sq. cm.
QED.