A concrete monument in the shape of a regular pyramid with a square base weighs 13,400 pounds. The monument is 7.30 feet high. Compute the length of a base side. Assume that concrete weighs 137 pounds per cubic foot.

To solve the problem of finding the side length of the square base of the concrete monument, let's follow these steps:

1. Determine the Volume of the Pyramid:
The weight of the concrete monument is 13,400 pounds. We know that concrete weighs 137 pounds per cubic foot. To find the volume of the pyramid, we use the formula:

[tex]\[
\text{Volume} = \frac{\text{Weight}}{\text{Weight per cubic foot}} = \frac{13400 \text{ pounds}}{137 \text{ pounds per cubic foot}}
\][/tex]

This gives us a volume of approximately 97.81 cubic feet.

2. Use the Formula for the Volume of a Pyramid:
The volume [tex]\(V\)[/tex] of a pyramid with a square base can be calculated using the formula:

[tex]\[
V = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\][/tex]

We already know the volume is about 97.81 cubic feet, and the height of the pyramid is 7.30 feet. Plugging in these values, we get:

[tex]\[
97.81 = \frac{1}{3} \times \text{Base Area} \times 7.30
\][/tex]

3. Solve for the Base Area:
To find the base area, rearrange the equation:

[tex]\[
\text{Base Area} = \frac{3 \times 97.81}{7.30}
\][/tex]

Calculating this gives us a base area of approximately 40.20 square feet.

4. Calculate the Side Length of the Base:
Since the base is a square, the side length [tex]\(s\)[/tex] can be found by taking the square root of the base area:

[tex]\[
s = \sqrt{\text{Base Area}} = \sqrt{40.20}
\][/tex]

This results in a side length of approximately 6.34 feet.

Thus, the length of a base side of the pyramid is approximately 6.34 feet.