# What is the least perimeter of a rectangle with an area of 32square. ft

Answer: The factors are 2,16,1,32,4 and 8. If it was 2 by 16, the perimeter would be 36. If it was 1 by 32, the perimeter would be 66. If it was 4 by 8, the perimeter would be 24. The smallest number is 24 so the smallest the perimeter could be is 24cm.
area=legnth timew width
32=area
32=LW
from experience, I know that the closer L is to W, the smaller the perimiter
so set L=W (this makes it a square and this is allowed since a square is a rectangle)

32=L^2=W^2
take square root
√32=L=W
4√2=L
perimiter=2L+2W
L=W
perimiter=2L+2L
p=4L

L=4√2
p=4(4√2)
P=16√2
aprox
22.63 ft

16√2 ft or 22.63 ft

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There are 75 houses in the troll's street. If in every 4th house there is a pink troll, a blue troll in every 6th house and a yellow troll in every 8th house, then in how many houses are there all of pink, blue and yellow trolls?

3

Explanation:

The problem is first to find the Least Common Multiple (LCM) for the numbers 4, 6 and 8 together.

To find the LCM, we have to break down every number into it's prime factors:

4: 2 x 2 = 2²

6: 2 x 3 = 2 x 3

8: 2 x 2 x 2 = 2³

Then for each prime number listed we pick the highest exponent and we multiply them.  For 2, the highest comes from 8 (2³), while for 3 there's only one occurrence... so the choice is easy:

LCM (4,6,8) = 2³ * 3 = 8 * 3 = 24

So, every 24 houses, we'll find all three trolls colors.

How many times will that happen within a group of 75 houses?

3 times of course, at houses #24, #48 and #72.

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Explanation:

Magnetic reversals have helped to support