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A square tile in a kitchen has an area of 121 square inches.

What is the length of one side of the square tile in inches?
(2 points)
Is this tile smaller or larger than a one foot by one foot tile?
What is the length of the square tile in inches?____
Is the tile smaller or larger than a one foot by one foot tile?____
:: 12
:: 11
:: 9
•: smaller
:: larger

7 answers

To find the length of one side of a square tile with an area of 121 square inches, you can take the square root of the area.

\[ \text{Length of one side} = \sqrt{121} = 11 \text{ inches} \]

Now, we compare this tile to a one-foot by one-foot tile. One foot is equal to 12 inches, so the area of a one-foot by one-foot tile is:

\[ 12 \text{ inches} \times 12 \text{ inches} = 144 \text{ square inches} \]

Since 121 square inches (the area of the tile) is less than 144 square inches, the tile is smaller than a one-foot by one-foot tile.

Therefore, the answers are:

Length of the square tile in inches: 11
Is the tile smaller or larger than a one foot by one foot tile? smaller

Which of these measurements has three significant digits? (1 point)
134 meters
• 56.09 inches
0.52 centimeters
• 8009 miles

To determine which of the given measurements has three significant digits, we need to analyze each option:

  1. 134 meters - This has three significant digits (1, 3, and 4).
  2. 56.09 inches - This has four significant digits (5, 6, 0, and 9).
  3. 0.52 centimeters - This has two significant digits (5 and 2).
  4. 8009 miles - This has four significant digits (8, 0, 0, and 9).

Therefore, the measurement that has three significant digits is:

134 meters.

Can the side lengths of a triangle be 3, 6 and 9? (1 point)
• yes
• no

To determine if the side lengths 3, 6, and 9 can form a triangle, you can use the Triangle Inequality Theorem. This theorem states that the sum of the lengths of any two sides must be greater than the length of the third side.

Let's check the three conditions:

  1. \( 3 + 6 > 9 \) → \( 9 > 9 \) (false)
  2. \( 3 + 9 > 6 \) → \( 12 > 6 \) (true)
  3. \( 6 + 9 > 3 \) → \( 15 > 3 \) (true)

The first condition is not satisfied, as \( 9 \) is not greater than \( 9 \). Therefore, the lengths 3, 6, and 9 cannot form a triangle.

The answer is: no.

The following side lengths, in meters, were given to a carpenter to build a front porch with a triangular design. The carpenter needs to determine which set of lengths will make a triangle to be able to use it in his design.
(Hint: Use the Triangle Inequality Theorem)
Option 1: Side lengths: 3, 3, 6
Option 2: Side lengths: 6, 8, 10
Option 3: Side lengths: 4, 6, 13 (1 point)
• Option 1
• Option 2
• Option 3

To determine which set of side lengths can form a triangle, we can use the Triangle Inequality Theorem. This theorem states that the sum of the lengths of any two sides must be greater than the length of the third side.

Let's check each option:

Option 1: Side lengths: 3, 3, 6

  • Check:
    1. \(3 + 3 > 6\) → \(6 > 6\) (false)
    2. \(3 + 6 > 3\) → \(9 > 3\) (true)
    3. \(3 + 6 > 3\) → \(9 > 3\) (true)

Since the first condition fails, these lengths cannot form a triangle.

Option 2: Side lengths: 6, 8, 10

  • Check:
    1. \(6 + 8 > 10\) → \(14 > 10\) (true)
    2. \(6 + 10 > 8\) → \(16 > 8\) (true)
    3. \(8 + 10 > 6\) → \(18 > 6\) (true)

All conditions are satisfied, so these lengths can form a triangle.

Option 3: Side lengths: 4, 6, 13

  • Check:
    1. \(4 + 6 > 13\) → \(10 > 13\) (false)
    2. \(4 + 13 > 6\) → \(17 > 6\) (true)
    3. \(6 + 13 > 4\) → \(19 > 4\) (true)

Since the first condition fails, these lengths cannot form a triangle.

Conclusion

The only option that satisfies the Triangle Inequality Theorem and can form a triangle is:

Option 2: Side lengths 6, 8, 10.