Question

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?

Answer 1

There are additional details to the problem that you have left out. I have found them in other resources. The tray has to be 3 centimeters high and the length is five centimeters longer than its width. The volume of the tray is 252 cubic centimeters.

With these given, we can find the equation with the width alone as the variable:

$V=lwh$
$252=(x+5)(x)(3)$
$84= x^{2} +5x$

To know if it's possible for the width to be 7.5 centimeters, we just plug this as the value of x and see if it satisfies the equation:

$84= (7.5)^{2} +5(7.5)$
$84= (7.5)^{2} +5(7.5)$
$84=93.75$

As we can see, the equation was not satisfied therefore it is NOT possible for the width to be 7.5 centimeters.