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zlopas [31]
3 years ago
15

Johanna used tiles to build a rectangular array with an area of 54. list all the possible dimension of the arrey

Mathematics
1 answer:
Advocard [28]3 years ago
4 0
Really this is an exercise in factorization. First find all the factors of 54: 1, 2, 3, 6, 9, 18, 27, 54

Then use each of those in a multiplication to get 54:

1×54
2×27
3×18
6x9

That's it. 4 possibilities.
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If we list all the natural numbers below 20 that are multiples of 7 or 11, we get 7, 11 and 14. The sum of these multiples is 32
velikii [3]
Number of multiples of 7 up to 1337: \left\lfloor\dfrac{1337}7\right\rfloor=191
Number of multiples of 11 up to 1337: \left\lfloor\dfrac{1337}{11}\right\rfloor=121
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This means there are 191+121-17=295 distinct multiples of 7 *or* 11 up to 1337.

The sum of these multiples is

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which can be computed using the well-known formula,

\displaystyle\sum_{k=1}^nk=\dfrac{n(n+1)}2

So you have

\displaystyle\sum_{k=1}^{191}7k+\sum_{k=1}^{121}11k-\sum_{k=1}^{17}77k=7\dfrac{191\times192}2+11\dfrac{121\times122}2-77\dfrac{17\times18}2=197762
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3 years ago
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