The volume of a rectangle box is 144 cubic inches. The height of the solid is 8 inches. Which measurements, in inches, could be the dimensions of the base?

Options

A. `3.3times5.5`
B. `2.5times7.2`
C. `12.0 times8.0`
D. `9.0times9.0`

Answer

To find the possible dimensions of the base of a rectangular box given its volume and height, we can follow these steps:

### Step 1: Understand the formula for the volume of a rectangular box.
The volume \( V \) of a rectangular box is given by the formula:
\[ V = L \times B \times H \]
where \( L \) is the length, \( B \) is the breadth (or width), and \( H \) is the height.

### Step 2: Substitute the known values into the formula.
We know that the volume \( V \) is 144 cubic inches and the height \( H \) is 8 inches. Therefore, we can substitute these values into the formula:
\[ 144 = L \times B \times 8 \]

### Step 3: Solve for \( L \times B \).
To find the product of the length and breadth, we can rearrange the equation:
\[ L \times B = \frac{144}{8} \]
Calculating this gives:
\[ L \times B = 18 \]

### Step 4: Check the options to find which pairs multiply to 18.
Now we need to check each of the provided options to see if their products equal 18.

- **Option 1:** \( 3.3 \times 5.5 \)
\[ 3.3 \times 5.5 = 18.15 \quad (\text{not equal to } 18) \]

- **Option 2:** \( 2.5 \times 7.2 \)
\[ 2.5 \times 7.2 = 18 \quad (\text{equal to } 18) \]

- **Option 3:** \( 12.0 \times 8.0 \)
\[ 12.0 \times 8.0 = 96 \quad (\text{not equal to } 18) \]

- **Option 4:** \( 9.0 \times 9.0 \)
\[ 9.0 \times 9.0 = 81 \quad (\text{not equal to } 18) \]

### Step 5: Conclusion
The only option that gives a product of 18 is **Option 2: 2.5 x 7.2**. Therefore, the dimensions of the base could be 2.5 inches and 7.2 inches.

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