Answer: Let's denote the length, width, and height of the cuboid as l, w, and h, respectively. We know that the shaded face is a square, which means that two of its dimensions are the same. Without loss of generality, let's assume that the dimensions of the square face are l and w.
Since the volume of the cuboid is 4900 cm³, we have:
lwh = 4900
Substituting l = 25 - w (since the length of the cuboid is 25 cm) and simplifying, we get:
(25 - w)w h = 4900
Now, we use the fact that the shaded face is a square. Since two of its dimensions are the same, we have:
l = w
Substituting this into the equation above, we get:
(25 - l)l h = 4900
Simplifying further, we have:
25l^2 - 4900 = 0
Solving for l using the quadratic formula, we get:
l = 14 or -14/5
Since the length of the cuboid cannot be negative, we have l = 14. Therefore, the length of one side of the square face is 14 cm.
Explanation: