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sdas [7]
3 years ago
14

Cynthia Besch wants to buy a rug for a room that is 19 ft wide and 32 ft long. She wants to leave a uniform strip of floor aroun

d the rug. She can afford to buy 420 square feet of carpeting. What dimensions should the rug have?

Mathematics
1 answer:
Rainbow [258]3 years ago
8 0

Answer:

The rug should be 15 ft wide and 28 ft long.

Step-by-step explanation:

I have attached a figure that represents the situation.

The the rug is l by h, the width of the strip of floor is w.

We are told that Cynthia can only afford 420 square feet of carpeting; therefore, it must be that

l*h=420 <em>(this says the area of the rug must be 420 square feet)</em>

From the figure we see that

l= 32-2w

h=19-2w

Therefore,

l*h=420\\\\(32-2w)(19-2w)=420

We expand this equation and get:

4w^2-102w+608=420\\\\4w^2-102w+188=0

using the quadratic equation we get two solutions:

w=2\\w=23.5

since the second solution, namely w=23.5, is larger than one of the dimensions of the room (is greater than 19 ft) it cannot be the width of the strip; therefore, we take w=2 to be our solution.

Now we find the dimensions of the rug:

l=32-2(2)=28\\\\h=19-2(2)=15

The rug is 15 ft wide and 28 ft long.

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love history [14]

If we know your Pythagorean Triples we can immediately recognize that the last choice is a right triangle:

8² + 15² = 17²

If you don't know your Pythagorean Triples, it's worth learning the first few off the list because teachers use them in problems all the time.  But for now let's just exhaustively check the Pythagorean Theorem for each triangle.  We don't have to multiply everything out; we can analyze the common factors.  If two have a common factor that the third one doesn't have, there's no way for the Pythagorean Theorem to add up.

Clearly 5²+15² is a multiple of 5 but 18² isn't so that one isn't a right triangle.

6²+12² is a multiple of 6, 16² isn't a multiple of 6, not an RT.

15²-5² is a multiple of 5, 13² isn't, no joy.

8²+15² = 64 + 225 = 289 = 17² -- that's a real right triangle, a valid Pythagorean Triple.

5 0
3 years ago
You have 80 pieces of fabric to make a wall hanging. Each piece of fabric is a square with a side length of 5 inches. You use as
tensa zangetsu [6.8K]
Okay. fist off don't think of them as 5 units each, but 1. so if you were to put it on graphing paper and box squares each time. you would be able to get 8 in for both sides to make a square. Area then would be 1600ft squared because 8 ×5 is 40 and 40×40 is 1600. then you calculate how many squares you used. 8×8=64. and 80-64=16 so 16 pieces are left over. then 9×9 (increasing the square) is 81. so 17 pieces to increase it.
5 0
3 years ago
Read 2 more answers
Om to 4conm.
max2010maxim [7]
The correct answer is water
8 0
3 years ago
How many ways can six friends be arranged around a circular dinner table?
Mice21 [21]
A question such as this one is a little tricky since the people seated are not in a straight line. 

For a circular table seating question, (n-1)! formula is used. Without restrictions 5! people can be seated. 

You might be wondering why it is not 6!, this is because the first person will the the 6 person so you are accounting for the same person twice. 

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3 years ago
Xan and Katie are twins. Xan weighs 66 6 6 pounds 99 9 9 ounces, and Katie weighs 88 8 8 pounds 11 1 1 ounce. What is the differ
gtnhenbr [62]

Answer:

264 ounces

Step-by-step explanation:

#Convert Xan weight into ounces:

1lb= 16 \ oz\\\\66\ lb=66\times 16=1056 \ oz\\\\\therefore Xan's=1056 \ oz+ 99 \ oz=1155 \ oz

Convert Katie's 88 pounds 11 ounce to ounces:

1lb= 16 \ oz\\\\88\ lb=88\times 16=1056 \ oz\\\\\therefore Katie's=1408 \ oz+ 11 \ oz=1419\ oz

The difference is calculated by subtracting Xan's from Katie's:

=1419 \ oz-1155 \ oz\\\\=264\ oz

Hence, the difference between the weights is 264 ounces

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3 years ago
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