Question

5.5: homework assignment
score: 0/33 answered: 0/33
question 33
suppose you need to build a box with a surface area of 2646 square feet.
the length of the box is 36 feet and the height will be 18 feet.
what is the width of the box?
a) let w = the width of the box. write the equation you would use to solve this problem.
b) now solve your equation
the width of the box must be feet.

Explanation:

Step1: Recall surface - area formula

The surface - area formula for a rectangular box is $SA = 2(lw+lh + wh)$, where $l$ is length, $w$ is width, and $h$ is height. Given $SA = 2646$, $l = 36$, and $h = 18$. Substitute these values into the formula: $2646=2(36w + 36\times18+18w)$.

Step2: Simplify the equation

First, simplify the expression inside the parentheses: $36w+36\times18 + 18w=36w + 648+18w=54w + 648$. Then the equation becomes $2646 = 2(54w + 648)$. Divide both sides of the equation by 2: $\frac{2646}{2}=54w + 648$, so $1323=54w + 648$.

Step3: Isolate the variable term

Subtract 648 from both sides: $1323−648 = 54w$, so $675 = 54w$.

Step4: Solve for $w$

Divide both sides by 54: $w=\frac{675}{54}=\frac{75}{6} = 12.5$.

Answer:

a) $2646 = 2(36w+36\times18 + 18w)$
b) $12.5$