Each side of a square office is 8 yards long. It will cost $49.90 per square yard to replace the carpet in the office. What would be the total cost to replace the carpet?

Question

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Answer 1

To find the total cost to replace the carpet in the square office, we first need to determine the area of the square.

1. Calculate the area of the square: The formula for the area \(A\) of a square is given by: \[ A = \text{side} \times \text{side} \] In this case, each side of the square is 8 yards: \[ A = 8 \times 8 = 64 \text{ square yards} \]

2. Calculate the total cost to replace the carpet: The cost per square yard is given as $49.90. To find the total cost \(C\), we multiply the area by the cost per square yard: \[ C = A \times \text{cost per square yard} \] Substituting the known values: \[ C = 64 \times 49.90 \] Now, we perform the multiplication: \[ C = 3199.36 \]

Therefore, the total cost to replace the carpet is: \[ \boxed{3199.36} \]

Answer 2

A rectangular sheet of metal measures 8 inches by 12 inches. The metal is worth $4.00 per square inch. How much is the sheet of metal worth?

$

Answer 3

To determine the value of the rectangular sheet of metal, we first need to calculate its area and then find the total cost based on the price per square inch.

1. Calculate the area of the rectangular sheet: The formula for the area \(A\) of a rectangle is given by: \[ A = \text{length} \times \text{width} \] Here, the length is 12 inches and the width is 8 inches: \[ A = 12 \times 8 = 96 \text{ square inches} \]

2. Calculate the total value of the metal: The cost per square inch is given as $4.00. To find the total value \(V\), multiply the area by the cost per square inch: \[ V = A \times \text{cost per square inch} \] Substituting the values we have: \[ V = 96 \times 4.00 = 384.00 \]

Therefore, the sheet of metal is worth: \[ \boxed{384.00} \]

Answer 4

The area of a rectangular sticker is 60 square centimeters. The sticker is 10 centimeters tall. How wide is it?

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centimeters

Answer 5

To find the width of the rectangular sticker, we can use the formula for the area of a rectangle:

\[ \text{Area} = \text{length} \times \text{width} \]

In this case, the area is given as 60 square centimeters, and the height (length) of the sticker is given as 10 centimeters. We can rearrange the formula to solve for the width:

\[ \text{width} = \frac{\text{Area}}{\text{length}} \]

Substituting the values we have:

\[ \text{width} = \frac{60}{10} = 6 \text{ centimeters} \]

Therefore, the width of the sticker is: \[ \boxed{6} \text{ centimeters} \]

Answer 6

A rectangular price tag is 8 centimeters wide and 5 centimeters tall. What is its area?

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square centimeters

Answer 7

To find the area of a rectangular price tag, you can use the formula for the area \(A\) of a rectangle:

\[ A = \text{width} \times \text{height} \]

Given that the width is 8 centimeters and the height is 5 centimeters, we can substitute these values into the formula:

\[ A = 8 \times 5 = 40 \text{ square centimeters} \]

Therefore, the area of the price tag is: \[ \boxed{40} \text{ square centimeters} \]