Question

select the correct answer from each drop - down menu. andy is designing a dice tray in the shape of a rectangular prism to use during a role - playing game. the tray needs to be three centimeters high and have a volume of 252 cubic centimeters in order for the dice to roll properly. the length of the tray should be five centimeters longer than its width. the volume of a rectangular prism is found using the formula v = l·w·h, where l is the length, w is the width, and h is the height. complete the equation that models the volume of the tray in terms of its width, x, in centimeters. x²+ x = is it possible for the width of the tray to be 7.5 centimeters? reset next

Explanation:

Step1: Define variables

Let width $x$, length $x + 5$, height $3$.

Step2: Write volume formula

$V=l\times w\times h=(x + 5)\times x\times3$.

Step3: Substitute volume value

$252=(x + 5)\times x\times3$.

Step4: Solve for $x$

$252 = 3x(x + 5)$, $84=x^{2}+5x$, $x^{2}+5x - 84=0$.
Factor: $(x + 12)(x - 7)=0$. So $x = 7$ or $x=-12$. Since width can't be negative, $x = 7$.

Answer:

Yes, it is possible as width can be 7 cm. Equation: $252=3x(x + 5)$