Question

a recycling bin is in the shape of a rectangular - box. find the height of the box if its length is 17 ft, its width is 5 ft, and its surface - area is 362 ft². (in the figure, h = height. assume that the given surface - area includes that of the top lid of the box.) the height of the box is ft.

Explanation:

Step1: Recall surface - area formula

The surface - area formula for a rectangular box is $S = 2(lw+lh + wh)$, where $l$ is the length, $w$ is the width, and $h$ is the height. Given $l = 17$ ft, $w = 5$ ft, and $S=362$ ft². Substitute these values into the formula: $362=2(17\times5 + 17h+5h)$.

Step2: Simplify the equation

First, simplify the expression inside the parentheses: $17\times5 = 85$, so the equation becomes $362 = 2(85+22h)$. Then, distribute the 2: $362=170 + 44h$.

Step3: Solve for $h$

Subtract 170 from both sides of the equation: $362−170=44h$, which gives $192 = 44h$. Then, divide both sides by 44: $h=\frac{192}{44}=\frac{48}{11}\approx4.36$ ft.

Answer:

$\frac{48}{11}$ ft