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.
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.
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