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Sphinxa [80]
3 years ago
15

ms Callahan is building a new dog pen for her dog. she has 24feet of fencing. the pen needs to be a rectangle. what is the lengt

h and width of the diffrent sizes of pens she can make with the amount of fencing
Mathematics
1 answer:
NeX [460]3 years ago
6 0
If Ms. Callahan has 24 feet of fencing, and she is building a pen, the PERIMETER of the pen must be 24 feet.  The perimeter is basically the distance around a figure.  The perimeter of a rectangle is equal to length plus width plus length plus width, AKA l+w+l+w, or P=2l+2w.  In a rectangle, two pairs of sides are of equal length--so the two lengths and the two widths must be equal.

So, the formula is P=2l+2w.  P, the perimeter, is 24, so 24=2l+2w.  Let's try some values for l and see what we get for w.  If the length is 1, l=1.  24=(2*1)+2w.  24=2+2w.  22=2w.  w=11.  So if length is 1 foot, width is 11 feet.

What if l=2?  24=(2*2)+2w.  24=4+2w.  2w=20.  w=10.  If l=2, w=10.  And l=3?  24=(2*3)+2w.  24=6+2w.  18=2w.  w=9.  If l=3, w=9.  Do you see a pattern?  Every time we add 1 to l, we subtract 1 from w.  So if l=4, w=8.  If l=5, w=7.  If l=6, w=6.  Here, we start getting similar answers: if l=7, w=5.  If l=8, w=4.  Since we already know these values work, it doesn't matter whether we call it length or width.  So, our answers are below.

Answer: Ms Callahan can make a pen with a length of 1 foot and a width of 11 feet, a length of 2 feet and a width of 10 feet, a length of 3 feet and a width of 9 feet, a length of 4 feet and a width of 8 feet, a length of 5 feet and a width of 7 feet, or a length of 6 feet and a width of 6 feet.
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Answer:

\huge\blue{ \mid{ \underline{ \overline{ \tt  ♡ ANSWER ♡ }} \mid}}

There's no specific formula to find the square root of a number, however we can find the square root of a number by the following methods:

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<h2><u>✏ By Prime Factorisation: </u></h2>

Step I: Obtain the given number.

Step II: Reduce the given number into prime factors by successive division.

Step III: Now make pairs of prime factors in such a way that both the factors in each pair are equal.

Step IV: Take one factor from each pair and find the product of these factors.

Step V: The product obtained by multiplying the factors is the required square root.

<h2><u>✏ Long Division:</u></h2>

Step 1: Firstly, we place a bar on every pair of digits starting from the unit digit. If the number of digits in it is odd, we put a bar on the single-digit too.

Step 2: Now we find the largest number whose square is less than or equal to the 1st number.

Step 3: Now we bring down the next bar number.

Step 4: For new divisor, we add the divisor & quotient.

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<h2><u>✏ Repeated subtraction method: </u></h2>

In this method, the given number is subtracted by 1, 3, 5, 7,… at every step till you get zero at the end. The number of steps in the solution is the required square root.

ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ

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