Question

1. length = (\frac{4}{1}) ft ; width = (\frac{5}{7}) ft ; height = (\frac{1}{5}) ft

Explanation:

Assuming the problem is to find the volume of a rectangular prism (since length, width, and height are given), the formula for the volume \( V \) of a rectangular prism is \( V = \text{length} \times \text{width} \times \text{height} \).

Step 1: Identify the formula for volume

The volume \( V \) of a rectangular prism is calculated by multiplying its length (\( l \)), width (\( w \)), and height (\( h \)):
\( V = l \times w \times h \)

Step 2: Substitute the given values

Given \( l = 4 \, \text{ft} \), \( w = \frac{5}{7} \, \text{ft} \), and \( h = \frac{1}{5} \, \text{ft} \), substitute these into the formula:
\( V = 4 \times \frac{5}{7} \times \frac{1}{5} \)

Step 3: Simplify the expression

First, multiply \( \frac{5}{7} \) and \( \frac{1}{5} \). The 5 in the numerator and 5 in the denominator cancel out:
\( \frac{5}{7} \times \frac{1}{5} = \frac{1}{7} \)

Then multiply this result by 4:
\( V = 4 \times \frac{1}{7} = \frac{4}{7} \)

Answer:

The volume is \( \frac{4}{7} \) cubic feet.