Answer: To find the dimensions of Andy's dice tray, use the given volume and the formula for the volume of a rectangular prism. Set up an equation using the width and length, then solve the equation to find the dimensions of the tray. The width of the tray is 7 centimeters and the length is 12 centimeters.
Step-by-step explanation: To find the dimensions of Andy's dice tray, we can use the formula for the volume of a rectangular prism: V = l · w · h. Since the height is given as 3 centimeters and the volume is given as 252 cubic centimeters, we can plug in these values and solve for the length and width of the tray. We are also given that the length is 5 centimeters longer than the width, so we can set up the equation l = w + 5.
Substituting the formula for volume and the equation for length into each other, we get 252 = (w + 5) · w · 3.
Expanding this equation gives us the quadratic equation 3w^2 + 15w - 252 = 0.
We can solve this equation by factoring or using the quadratic formula.
The solutions are w = 7 and w = -12,
but since the width cannot be negative, we can discard the negative solution.
Therefore, the width of the tray is 7 centimeters, and the length is 7 + 5 = 12 centimeters.