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Math Experts pls help?
A wire of length 6m is cut to form 15 squares and arranged in order of increasing size. Suppose the difference between the perimeters of any two consecutive squares is 4cm, find the length in cm of the side of the smallest square.
2 Answers
- mizooLv 72 years agoFavorite Answer
6 meter = 600 cm
1: perimeter of the smallest square: x
2: x + 4
3: x + 8
4: x + 12
...
15: perimeter of the largest square: x + (14 * 4) = x + 56
x + (x + 4) + (x + 8) + ... + (x + 56) = 600
15x + (4 + 56) * 14/2 = 600
15x + 420 = 600
x = 12 cm
=> 12/4 = 3 cm
- RealProLv 72 years ago
Perimeter of smallest square = P cm
Perimeter of largest square = P + 14*4 cm
What is the formula for the sum of an arithmetic sequence?
Sum = average of first and last multiplied by number of terms
600 = 15(P + P+14*4) / 2
P = (2*600 / 15 - 14*4) / 2
The required side is 1/4 of that.
