The volume of a rectangular prism can be calculated with the formula V=lwh

Question

, where V
is the volume, l
is the length, w
is the width, and h
is the height. If a rectangular prism has a volume of 90 ft.3
, length of 3 ft., and height of 12 ft., what is its width? Enter your answer as a decimal.(1 point)
ft.

Answer 1

To find the width of the rectangular prism, we can use the volume formula:

\[ V = l \times w \times h \]

We know:

• \( V = 90 , \text{ft}^3 \)
• \( l = 3 , \text{ft} \)
• \( h = 12 , \text{ft} \)

We need to solve for \( w \):

\[ 90 = 3 \times w \times 12 \]

First, calculate \( 3 \times 12 \):

\[ 3 \times 12 = 36 \]

Now we can rewrite the equation:

\[ 90 = 36 \times w \]

To isolate \( w \), divide both sides by 36:

\[ w = \frac{90}{36} \]

Now simplify the fraction:

\[ w = \frac{90 \div 18}{36 \div 18} = \frac{5}{2} = 2.5 \]

Therefore, the width \( w \) is:

\[ \boxed{2.5} , \text{ft} \]

Answer 2

The area of a rectangle is calculated with the formula A=lw. If the area of a rectangle is 52.5 m2 and the width is 5 m, what is the length? Explain the solution to the real-world problem.(1 point)
Responses

The length is 10.5 m.
The length is 10.5 m.

The length is 262.5 m2.
The length is 262.5 m squared .

l=10.5
l equals 10.5

The length is 262.5 m.

Answer 3

To find the length of a rectangle given the area and the width, we can use the formula for the area of a rectangle:

\[ A = l \times w \]

where:

• \( A \) is the area,
• \( l \) is the length,
• \( w \) is the width.

In this case, we are given:

• \( A = 52.5 , \text{m}^2 \)
• \( w = 5 , \text{m} \)

We need to solve for \( l \):

1. Plug the values into the formula:

\[ 52.5 = l \times 5 \]

2. To isolate \( l \), divide both sides by 5:

\[ l = \frac{52.5}{5} \]

3. Calculate \( l \):

\[ l = 10.5 , \text{m} \]

So, the length \( l \) is \( 10.5 , \text{m} \).

Explanation of the Solution:

In the context of a real-world problem, if we think about a rectangular garden that has an area of 52.5 square meters and a width of 5 meters, we can determine that the length of the garden must be 10.5 meters to achieve that area. This information can help a gardener or planner know exactly how much length is needed to fit the desired area for planting.

The correct response is:

The length is 10.5 m.