Two identical rectangular prisms each have a height of 40 centimeters. The base of each prism is a square, and the surface area of each prism is M cm2𝑀 cm2. If the prisms are glued together along a square base, the resulting prism has a surface area of 95M cm295𝑀 cm2. What is the side length, in cmcm, of each square base? 2eliminate4eliminate8eliminate20

The surface area of a rectangular prism is given by the formula 2lw + 2lh + 2wh, where l is the length, w is the width, and h is the height.

Since the base of each prism is a square, the length and width are equal, so we can simplify the formula to 2s^2 + 4sh, where s is the side length of the square base.

Given that the surface area of each prism is M cm^2, we can write the equation as M = 2s^2 + 4s*40.

When the two prisms are glued together along a square base, the height of the resulting prism is 80 cm (since each prism has a height of 40 cm). The surface area of the resulting prism is given by the formula 2s^2 + 4s*80.

According to the problem, the surface area of the resulting prism is 95M cm^2. So we can write the equation as 95M = 2s^2 + 4s*80.

We can solve this system of equations to find the value of s.

First, we can simplify the first equation to M = 2s^2 + 160s.

Then, we can substitute M from the first equation into the second equation to get 95(2s^2 + 160s) = 2s^2 + 320s.

Solving this equation gives s = 20 cm.

So, the side length of each square base is 20 cm.