Rectangles Tangle
There are two rectangles: A and B. Rectangle A: Length = 40 cm, Diagonal = 41 cm.
Rectangle B: Breadth = 5 cm, Diagonal = 13 cm.
What is the sum of the areas and perimeters of both the rectangles?
The answer is 552.
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2 solutions
By pythagorean theorem, we have
x = 4 1 2 − 4 0 2 = 9
y = 1 3 2 − 5 2 = 1 2
The area of the first rectangle is 9 ( 4 0 ) = 3 6 0 . The perimeter of the first rectangle is 2 ( 9 ) + 2 ( 4 0 ) = 9 8
The area of the second rectangle is 1 2 ( 5 ) = 6 0 . The perimeter of the second rectangle is 2 ( 5 ) + 2 ( 1 2 ) = 3 4 .
Hence, the numerical sum of the areas and perimeters is 3 6 0 + 9 8 + 6 0 + 3 4 = 5 5 2
radq(41^2-40^2)=9; radq(13^2-5^2)=12. 9x40+5x12+2x(9+40+5+12)=552