A square pyramid has a surface area of 175 square inches. The square base has side lengths of 5 inches. Find the slant height of the pyramid.

To find the slant height of the square pyramid, we can use the formula for the surface area of a square pyramid and solve for the slant height.

The surface area of a square pyramid is given by the formula:
SA = B + 4 * (1/2 * P * slant height)

where SA is the surface area, B is the base area, P is the perimeter of the base, and the slant height is the height of each triangular face.

In this case, we are given that the surface area (SA) is 175 square inches, the base of the pyramid is a square with side lengths of 5 inches, and the number of triangular faces is 4.

First, let's determine the base area (B) and the perimeter of the base (P):
B = side length * side length
= 5 inches * 5 inches
= 25 square inches

P = 4 * side length
= 4 * 5 inches
= 20 inches

Now we can substitute the values into the surface area formula and solve for the slant height:
175 = 25 + 4 * (1/2 * 20 inches * slant height)

Simplifying the equation:
175 = 25 + 40 inches * slant height

150 = 40 inches * slant height

Dividing both sides by 40 inches:
slant height = 150 / 40 inches

Simplifying:
slant height = 3.75 inches

Therefore, the slant height of the square pyramid is 3.75 inches.