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pickupchik [31]
3 years ago
10

The length of a rectangle is 4cm less than twice its width. The perimeter of the rectangle is 58cm. What is the length of the re

ctangle?
Mathematics
1 answer:
LiRa [457]3 years ago
6 0

11 centimeters is the answer

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find the least length of a rod which can be cut into exactly epual strips,each of either 36cm or 42cm in length​
Triss [41]

Step-by-step explanation:

so, we need to find the smallest common multiple of 36 and 42.

that is the smallest number I can divide both by 36 and 42 without remain.

let's use the method of basic prime factors (we start with the smallest fitting prime number - 2 is a prime number too - and divide as often as possible, then continue with the next bigger prime number, until there is nothing left to divide) :

36 / 2 = 18

18 / 2 = 9

9 / 3 = 3

3 / 3 = 1 finished

therefore,

36 = 2×2×3×3

42 / 2 = 21

21 / 3 = 7

7 / 5 does not work

7 / 7 = 1 finished

therefore,

42 = 2×3×7

to find the smallest common multiple (SCM) we check the maximum length of each prime factor sequence.

and we see 2 times 2, 2 times 3 and 1 time 7.

so, the SCM = 2×2×3×3×7 = 252.

there is no smaller number that can be divided by both 36 and 42 without remain.

so, the rod must be at least 252 cm long to cut it into equally long pieces of either 36 cm (7 pieces) or 42 cm (6 pieces).

5 0
3 years ago
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