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notsponge [240]
3 years ago
10

Cynthia Besch wants to buy a rug for a room that is 20 ft wide and 26 ft long. She wants to leave a uniform strip of floor aroun

d the rug. She can afford to buy 352 square feet of carpeting. What dimensions should the rug​ have?
Mathematics
1 answer:
Radda [10]3 years ago
4 0

Answer:

16 ft by 22 ft

Step-by-step explanation:

The Area of the carpeting she must have = 352 ft²

To solve for this, we have:

Length × Width = Area of a rectangle

352ft² = Length × Width

352ft² = (20 - x) (26 - x)

352 = 520 - 20x - 26x + x²

352 = 520 - 46x + x²

Collect like terms

x² - 46x + 520 - 352

x² - 46x + 168

We factorise

x² - 4x - 42x + 106

(x² - 4x) -(42x + 106)

x(x - 4) -42(x - 4)

(x - 4)(x - 42)

x - 4 = 0, x = 4

x - 42 = 0, x = 42

We choose the least value for x

Hence, x = 4

Length = 20 - 4 = 16ft

Width = 22- 4= 22ft

The dimensions the rug should have is 16ft by 22 ft, meaning 16ft wide and 22ft long

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Given:

Consider the below table attached with this question.

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Solution:

We have,

1 square meter of ceiling =  10.75 tiles.      ...(i)

Therefore, the number of tiles corresponding to 1 square meter of ceiling is 10.75.

Multiply both sides by 10.

10×1 square meter of ceiling =  10×10.75 tiles.

10 square meter of ceiling =  107.5 tiles.

Therefore, the number of tiles corresponding to 10 square meter of ceiling is 107.5.

Divide both sides by 10.75 in (i).

\dfrac{1}{10.75} square meter of ceiling = 1 tile.

Multiply both sides by 100.

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On approximating the value, we get

9.3 square meter of ceiling = 100 tiles.

Therefore, the square meters of ceiling corresponding to 100 tiles is about 9.3.

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a square meter of ceiling =  10.75a tiles.

Therefore, the number of tiles corresponding to a square meter of ceiling is 10.75a.

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Answer:

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We must write the data problems.

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<u>Solution:</u>

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