You have an 24 cm long string. Examine if you can cut in two parts and create a) Two squares b) Two circles

misyjny76 2022-09-27 Answered
You have an 24 cm long string. Examine if you can cut in two parts and create
a) Two squares
b) Two circles
whose total area is 20 cm 2 . (The entire length must be used)
It says the string is cut into 2 parts, and not 2 equal parts.
So for 2 squares: The sum of perimeters will be 24 cm. That's,
4 l 1 + 4 l 2 = 24 and l 1 2 + l 2 2 = 20
Similarly, For 2 circles:
2 π r 1 + 2 π r 2 = 24 and π r 1 2 + π r 2 2 = 20
I get 2 equations and 2 unknowns, how do I solve these equations?
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Answers (1)

Lorenzo Acosta
Answered 2022-09-28 Author has 13 answers
Note that from the first equation (part a) we have l 2 = 6 l 1 . Now plug the l 2 into the other equation: l 1 2 + ( 6 l 1 ) 2 = 20. This is a quadratic which we solve:
l 1 2 + ( 36 12 l 1 + l 1 2 ) = 20 2 l 1 2 12 l 1 + 16 = 0 l 1 2 6 l 1 + 8 = 0 ( l 1 4 ) ( l 1 2 ) = 0
Therefore l 1 = 2 and l 2 = 6 l 1 = 4 or l 1 = 4 and l 2 = 6 l 1 = 2. That just means one square has side length 2 and the other has side length 4.
Apply the same method (called substition) for the second set of equations.
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