The volume of a rectangular box is x³+16x²+83x+140cm³. The box is x +5 cm long and x+7 cm wide. How tall is the box?
Solve for h.
To find the height (h) of the box, we first need to find the volume of the box using the given dimensions and then set it equal to x³+16x²+83x+140cm³.
The volume of a rectangular box is given by the formula V = lwh, where l is the length, w is the width, and h is the height.
Given:
l = x + 5 cm
w = x + 7 cm
V = x³ + 16x² + 83x + 140 cm³
Substitute the given values into the formula:
(x + 5)(x + 7)h = x³ + 16x² + 83x + 140
Expand the left side of the equation:
x² + 12x + 35h = x³ + 16x² + 83x + 140
Rearrange the equation to set it equal to zero:
x³ + 3x² - 71x - 140 = 0
This is a cubic equation that can be solved to find the value of x, which will be the height of the box. The solution for x will give us the height of the box.