Hi! I'd be happy to help you find the length of the tank. To find the length, we'll use the formula for the volume of a rectangular prism: Volume = Length × Width × Height.
The volume of the tank is 126 cubic yards, the width is 2 2/5 yards, and the height is 2 4/5 yards. First, let's convert the mixed numbers to improper fractions:
Width: 2 2/5 = (2 × 5 + 2) / 5 = 12/5 yards
Height: 2 4/5 = (2 × 5 + 4) / 5 = 14/5 yards
Now, we'll plug these values into the volume formula and solve for the length:
126 = Length × (12/5) × (14/5)
To isolate the length, divide both sides of the equation by (12/5) × (14/5):
Length = 126 / [(12/5) × (14/5)]
Length = 126 × (5/12) × (5/14)
Length = (126 × 5 × 5) / (12 × 14)
Length = 630 / (168)
Length = 3.75 yards
The length of the tank is 3.75 yards.